Verfügbarkeit: Mathematical methods of quantum optics

Mathematical methods of quantum optics:

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Puri, Ravinder Rupchand 1950- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2001
Schriftenreihe:	Springer series in optical sciences 79
Schlagworte:	Quantenoptik - Mathematische Methode Quantenoptik - Mathematische Physik Mathematik Mathematische Physik Mathematical physics Quantum optics > Mathematics Mathematische Methode Quantenoptik
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIII, 285 S.
ISBN:	3540678026

Internformat

MARC


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245	1	0	\|a Mathematical methods of quantum optics \|c Ravinder R. Puri
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Datensatz im Suchindex

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adam_text	CONTENTS 1. BASIC QUANTUM MECHANICS ................................ 1 1.1 POSTULATES OF QUANTUM MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 POSTULATE 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 POSTULATE 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.3 POSTULATE 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.4 POSTULATE 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.5 POSTULATE 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2 GEOMETRIC PHASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.1 GEOMETRIC PHASE OF A HARMONIC OSCILLATOR . . . . . . . . . . . 18 1.2.2 GEOMETRIC PHASE OF A TWO-L EVEL SYSTEM . . . . . . . . . . . . 18 1.2.3 GEOMETRIC PHASE IN ADIABATIC EVOLUTION . . . . . . . . . . . . 18 1.3 TIME-DEPENDENT APPROXIMATION METHOD . . . . . . . . . . . . . . . . . . 19 1.4 QUANTUM MECHANICS OF A COMPOSITE SYSTEM . . . . . . . . . . . . . . . 20 1.5 QUANTUM MECHANICS OF A SUBSYSTEM AND DENSITY OPERATOR . . 21 1.6 SYSTEMS OF ONE AND TWO SPIN-1/2S . . . . . . . . . . . . . . . . . . . . . . . 23 1.7 WAVEPARTICLE DUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.8 MEASUREMENT POSTULATE AND PARADOXES OF QUANTUM THEORY . . 29 1.8.1 THE MEASUREMENT PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . 30 1.8.2 SCHR¨ ODINGERS CAT PARADOX. . . . . . . . . . . . . . . . . . . . . . . . . 31 1.8.3 EPR PARADOX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.9 L OCAL HIDDEN VARIABLES THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2. ALGEBRA OF THE EXPONENTIAL OPERATOR ..................... 37 2.1 PARAMETRIC DIFFERENTIATION OF THE EXPONENTIAL . . . . . . . . . . . . . . 37 2.2 EXPONENTIAL OF A FINITE-DIMENSIONAL OPERATOR . . . . . . . . . . . . . . 38 2.3 L IE ALGEBRAIC SIMILARITY TRANSFORMATIONS . . . . . . . . . . . . . . . . . . 39 2.3.1 HARMONIC OSCILLATOR ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . 41 2.3.2 THE SU (2) ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3.3 THE SU (1,1) ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3.4 THE SU ( M ) ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.3.5 THE SU ( M, N ) ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.4 DISENTANGLING AN EXPONENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.4.1 THE HARMONIC OSCILLATOR ALGEBRA . . . . . . . . . . . . . . . . . . . 49 2.4.2 THE SU (2) ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 X CONTENTS 2.4.3 SU (1,1) ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.5 TIME-ORDERED EXPONENTIAL INTEGRAL . . . . . . . . . . . . . . . . . . . . . . . 52 2.5.1 HARMONIC OSCILLATOR ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . 52 2.5.2 SU (2) ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.5.3 THE SU (1,1) ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3. REPRESENTATIONS OF SOME LIE ALGEBRAS .................... 55 3.1 REPRESENTATION BY EIGENVECTORS AND GROUP PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.1.1 BASES CONSTITUTED BY EIGENVECTORS . . . . . . . . . . . . . . . . . . 55 3.1.2 BASES L ABELED BY GROUP PARAMETERS . . . . . . . . . . . . . . . . 56 3.2 REPRESENTATIONS OF HARMONIC OSCILLATOR ALGEBRA . . . . . . . . . . . . 60 3.2.1 ORTHONORMAL BASES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.2.2 MINIMUM UNCERTAINTY COHERENT STATES . . . . . . . . . . . . . . 61 3.3 REPRESENTATIONS OF SU (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3.1 ORTHONORMAL REPRESENTATION . . . . . . . . . . . . . . . . . . . . . . . 68 3.3.2 MINIMUM UNCERTAINTY COHERENT STATES . . . . . . . . . . . . . . 70 3.4 REPRESENTATIONS OF SU (1 , 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.4.1 ORTHONORMAL BASES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.4.2 MINIMUM UNCERTAINTY COHERENT STATES . . . . . . . . . . . . . . 77 4. QUASIPROBABILITIES AND NON-CLASSICAL STATES ............... 81 4.1 PHASE SPACE DISTRIBUTION FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 PHASE SPACE REPRESENTATION OF SPINS . . . . . . . . . . . . . . . . . . . . . . 88 4.3 QUASIPROBABILITIY DISTRIBUTIONS FOR EIGENVALUES OF SPIN COMPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4 CLASSICAL AND NON-CLASSICAL STATES . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.4.1 NON-CLASSICAL STATES OF ELECTROMAGNETIC FIELD . . . . . . . . 95 4.4.2 NON-CLASSICAL STATES OF SPIN-1/2S . . . . . . . . . . . . . . . . . . . 97 5. THEORY OF STOCHASTIC PROCESSES ........................... 99 5.1 PROBABILITY DISTRIBUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 MARKOV PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.3 DETAILED BALANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.4 LIOUVILLE AND FOKKERPLANCK EQUATIONS . . . . . . . . . . . . . . . . . . . . 106 5.4.1 LIOUVILLE EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.4.2 THE FOKKERPLANCK EQUATION . . . . . . . . . . . . . . . . . . . . . . 107 5.5 STOCHASTIC DIFFERENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.6 L INEAR EQUATIONS WITH ADDITIVE NOISE . . . . . . . . . . . . . . . . . . . . . 110 5.7 L INEAR EQUATIONS WITH MULTIPLICATIVE NOISE . . . . . . . . . . . . . . . . 112 5.7.1 UNIVARIATE LINEAR MULTIPLICATIVE STOCHASTIC DIFFEREN- TIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.7.2 MULTIVARIATE LINEAR MULTIPLICATIVE STOCHASTIC DIFFER- ENTIAL EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.8 THE POISSON PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 CONTENTS XI 5.9 STOCHASTIC DIFFERENTIAL EQUATION DRIVEN BY RANDOM TELEGRAPH NOISE . . . . . . . . . . . . . . . . . . . . . . . 116 6. THE ELECTROMAGNETIC FIELD ................................ 119 6.1 FREE CLASSICAL FIELD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.2 FIELD QUANTIZATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.3 STATISTICAL PROPERTIES OF CLASSICAL FIELD . . . . . . . . . . . . . . . . . . . . 123 6.3.1 FIRST-ORDER CORRELATION FUNCTION . . . . . . . . . . . . . . . . . . . 125 6.3.2 SECOND-ORDER CORRELATION FUNCTION . . . . . . . . . . . . . . . . . 126 6.3.3 HIGHER-ORDER CORRELATIONS . . . . . . . . . . . . . . . . . . . . . . . . . 126 6.3.4 STABLE AND CHAOTIC FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.4 STATISTICAL PROPERTIES OF QUANTIZED FIELD . . . . . . . . . . . . . . . . . . . 130 6.4.1 FIRST-ORDER CORRELATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.4.2 SECOND-ORDER CORRELATION . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.4.3 QUANTIZED COHERENT AND THERMAL FIELDS . . . . . . . . . . . . 132 6.5 HOMODYNED DETECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6.6 SPECTRUM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7. ATOMFIELD INTERACTION HAMILTONIANS ..................... 137 7.1 DIPOLE INTERACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.2 ROTATING WAVE AND RESONANCE APPROXIMATIONS . . . . . . . . . . . . . 140 7.3 TWO-L EVEL ATOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.4 THREE-L EVEL ATOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 7.5 EFFECTIVE TWO-L EVEL ATOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 7.6 MULTI-CHANNEL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 7.7 PARAMETRIC PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 7.8 CAVITY QED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 7.9 MOVING ATOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 8. QUANTUM THEORY OF DAMPING ............................. 155 8.1 THE MASTER EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.2 SOLVING A MASTER EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 8.3 MULTI-TIME AVERAGE OF SYSTEM OPERATORS . . . . . . . . . . . . . . . . . . 162 8.4 BATH OF HARMONIC OSCILLATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 8.4.1 THERMAL RESERVOIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.4.2 SQUEEZED RESERVOIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.4.3 RESERVOIR OF THE ELECTROMAGNETIC FIELD . . . . . . . . . . . . . . 167 8.5 MASTER EQUATION FOR A HARMONIC OSCILLATOR . . . . . . . . . . . . . . . . 168 8.6 MASTER EQUATION FOR TWO-L EVEL ATOMS . . . . . . . . . . . . . . . . . . . . 170 8.6.1 TWO-L EVEL ATOM IN A MONOCHROMATIC FIELD . . . . . . . . . . 171 8.6.2 COLLISIONAL DAMPING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 8.7 MASTER EQUATION FOR A THREE-L EVEL ATOM . . . . . . . . . . . . . . . . . . 173 8.8 MASTER EQUATION FOR FIELD INTERACTING WITH A RESERVOIR OF ATOMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 XII CONTENTS 9. LINEAR AND NONLINEAR RESPONSE OF A SYSTEM IN AN EXTERNAL FIELD ...................................... 177 9.1 STEADY STATE OF A SYSTEM IN AN EXTERNAL FIELD. . . . . . . . . . . . . . 177 9.2 OPTICAL SUSCEPTIBILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 9.3 RATE OF ABSORPTION OF ENERGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 9.4 RESPONSE IN A FLUCTUATING FIELD . . . . . . . . . . . . . . . . . . . . . . . . . . 183 10. SOLUTION OF LINEAR EQUATIONS: METHOD OF EIGENVECTOR EXPANSION ........................ 185 10.1 EIGENVALUES AND EIGENVECTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 10.2 GENERALIZED EIGENVALUES AND EIGENVECTORS . . . . . . . . . . . . . . . . . 189 10.3 SOLUTION OF TWO-TERM DIFFERENCE-DIFFERENTIAL EQUATION . . . . . . 191 10.4 EXACTLY SOLVABLE TWO- AND THREE-TERM RECURSION RELATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 10.4.1 TWO-TERM RECURSION RELATIONS . . . . . . . . . . . . . . . . . . . . . 192 10.4.2 THREE-TERM RECURSION RELATIONS . . . . . . . . . . . . . . . . . . . 193 11. TWO-LEVEL AND THREE-LEVEL HAMILTONIAN SYSTEMS .................... 199 11.1 EXACTLY SOLVABLE TWO-L EVEL SYSTEMS . . . . . . . . . . . . . . . . . . . . . . 199 11.1.1 TIME-INDEPENDENT DETUNING AND COUPLING . . . . . . . . . . . 202 11.1.2 ON-RESONANT REAL TIME-DEPENDENT COUPLING . . . . . . . . 208 11.1.3 FLUCTUATING COUPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 11.2 N TWO-L EVEL ATOMS IN A QUANTIZED FIELD . . . . . . . . . . . . . . . . . 210 11.3 EXACTLY SOLVABLE THREE-L EVEL SYSTEMS . . . . . . . . . . . . . . . . . . . . . 210 11.4 EFFECTIVE TWO-L EVEL APPROXIMATION . . . . . . . . . . . . . . . . . . . . . . . 212 12. DISSIPATIVE ATOMIC SYSTEMS ............................... 215 12.1 TWO-L EVEL ATOM IN A QUASIMONOCHROMATIC FIELD . . . . . . . . . . . 215 12.1.1 TIME-DEPENDENT EVOLUTION OPERATOR REDUCIBLE TO SU (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 12.1.2 TIME-INDEPENDENT EVOLUTION OPERATOR . . . . . . . . . . . . . . 219 12.1.3 NONLINEAR RESPONSE IN A BICHROMATIC FIELD . . . . . . . . . . 223 12.2 N TWO-L EVEL ATOMS IN A MONOCHROMATIC FIELD . . . . . . . . . . . . . 224 12.3 TWO-L EVEL ATOMS IN A FLUCTUATING FIELD . . . . . . . . . . . . . . . . . . . 236 12.4 DRIVEN THREE-L EVEL ATOM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 13. DISSIPATIVE FIELD DYNAMICS ............................... 239 13.1 DOWN-CONVERSION IN A DAMPED CAVITY . . . . . . . . . . . . . . . . . . . . 239 13.1.1 AVERAGES AND VARIANCES OF THE CAVITY FIELD OPERATORS 240 13.1.2 DENSITY MATRIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 13.2 FIELD INTERACTING WITH A TWO-PHOTON RESERVOIR . . . . . . . . . . . . . 245 13.2.1 TWO-PHOTON ABSORPTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 13.2.2 TWO-PHOTON GENERATION AND ABSORPTION . . . . . . . . . . . . 247 13.3 RESERVOIR IN THE L AMBDA CONFIGURATION . . . . . . . . . . . . . . . . . . . . 248 CONTENTS XIII 14. DISSIPATIVE CAVITY QED .................................. 251 14.1 TWO-L EVEL ATOMS IN A SINGLE-MODE CAVITY . . . . . . . . . . . . . . . . . 251 14.2 STRONG ATOMFIELD COUPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 14.2.1 SINGLE TWO-L EVEL ATOM . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 14.3 RESPONSE TO AN EXTERNAL FIELD . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 14.3.1 L INEAR RESPONSE TO A MONOCHROMATIC FIELD . . . . . . . . . . 256 14.3.2 NONLINEAR RESPONSE TO A BICHROMATIC FIELD . . . . . . . . . . 257 14.4 THE MICROMASER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 14.4.1 DENSITY OPERATOR OF THE FIELD . . . . . . . . . . . . . . . . . . . . . . 259 14.4.2 TWO-L EVEL ATOMIC MICROMASER . . . . . . . . . . . . . . . . . . . . . 263 14.4.3 ATOMIC STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 APPENDICES ................................................... 267 A. SOME MATHEMATICAL FORMULAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 B. HYPERGEOMETRIC EQUATION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 C. SOLUTION OF TWO- AND THREE-DIMENSIONAL L INEAR EQUATIONS . . . . . . . . . . . . . . . . . . 272 D. ROOTS OF A POLYNOMIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 REFERENCES .................................................... 277 INDEX ......................................................... 283
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isbn	3540678026
language	English
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physical	XIII, 285 S.
publishDate	2001
publishDateSearch	2001
publishDateSort	2001
publisher	Springer
record_format	marc
series	Springer series in optical sciences
series2	Springer series in optical sciences Physics and astronomy online library
spelling	Puri, Ravinder Rupchand 1950- Verfasser (DE-588)122132084 aut Mathematical methods of quantum optics Ravinder R. Puri Berlin [u.a.] Springer 2001 XIII, 285 S. txt rdacontent n rdamedia nc rdacarrier Springer series in optical sciences 79 Physics and astronomy online library Quantenoptik - Mathematische Methode Quantenoptik - Mathematische Physik Mathematik Mathematische Physik Mathematical physics Quantum optics Mathematics Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Quantenoptik (DE-588)4047990-0 gnd rswk-swf Quantenoptik (DE-588)4047990-0 s Mathematische Methode (DE-588)4155620-3 s DE-604 Mathematische Physik (DE-588)4037952-8 s Springer series in optical sciences 79 (DE-604)BV000000237 79 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009060886&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Puri, Ravinder Rupchand 1950- Mathematical methods of quantum optics Springer series in optical sciences Quantenoptik - Mathematische Methode Quantenoptik - Mathematische Physik Mathematik Mathematische Physik Mathematical physics Quantum optics Mathematics Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Quantenoptik (DE-588)4047990-0 gnd
subject_GND	(DE-588)4155620-3 (DE-588)4037952-8 (DE-588)4047990-0
title	Mathematical methods of quantum optics
title_auth	Mathematical methods of quantum optics
title_exact_search	Mathematical methods of quantum optics
title_full	Mathematical methods of quantum optics Ravinder R. Puri
title_fullStr	Mathematical methods of quantum optics Ravinder R. Puri
title_full_unstemmed	Mathematical methods of quantum optics Ravinder R. Puri
title_short	Mathematical methods of quantum optics
title_sort	mathematical methods of quantum optics
topic	Quantenoptik - Mathematische Methode Quantenoptik - Mathematische Physik Mathematik Mathematische Physik Mathematical physics Quantum optics Mathematics Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Quantenoptik (DE-588)4047990-0 gnd
topic_facet	Quantenoptik - Mathematische Methode Quantenoptik - Mathematische Physik Mathematik Mathematische Physik Mathematical physics Quantum optics Mathematics Mathematische Methode Quantenoptik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009060886&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000237
work_keys_str_mv	AT puriravinderrupchand mathematicalmethodsofquantumoptics

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