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Path integrals in quantum mechanics /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
2010.
|
| Colección: | Oxford graduate texts.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""Cover""; ""Contents""; ""1 Gaussian integrals""; ""1.1 Generating function""; ""1.2 Gaussian expectation values. Wick�s theorem""; ""1.3 Perturbed gaussian measure. Connected contributions""; ""1.4 Expectation values. Generating function. Cumulants""; ""1.5 Steepest descent method""; ""1.6 Steepest descent method: several variables, generating functions""; ""1.7 Gaussian integrals: complex matrices""; ""Exercises""; ""2 Path integrals in quantum mechanics""; ""2.1 Local markovian processes""; ""2.2 Solution of the evolution equation for short times""; ""2.3 Path integral representation""
- ""2.4 Explicit calculation: gaussian path integrals""""2.5 Correlation functions: generating functional""; ""2.6 General gaussian path integral and correlation functions""; ""2.7 Quantum harmonic oscillator: the partition function""; ""2.8 Perturbed harmonic oscillator""; ""2.9 Perturbative expansion in powers of ħ""; ""2.10 Semi-classical expansion""; ""Exercises""; ""3 Partition function and spectrum""; ""3.1 Perturbative calculation""; ""3.2 Semi-classical or WKB expansion""; ""3.3 Path integral and variational principle""; ""3.4 O(N) symmetric quartic potential for N â?? â?ž""
- 3.5 Operator determinants3.6 Hamiltonian: structure of the ground state
- Exercises
- 4 Classical and quantum statistical physics
- 4.1 Classical partition function. Transfer matrix
- 4.2 Correlation functions
- 4.3 Classical model at low temperature: an example
- 4.4 Continuum limit and path integral
- 4.5 The two-point function: perturbative expansion, spectral representation
- 4.6 Operator formalism. Time-ordered products
- Exercises
- 5 Path integrals and quantization
- 5.1 Gauge transformations
- ""5.2 Coupling to a static magnetic field: gauge symmetry""""5.3 Quantization and path integrals""; ""5.4 Static magnetic field: direct calculation""; ""5.5 Diffusion, random walk, Fokker�Planck equation""; ""5.6 The spectrum of the O(2) rigid rotator""; ""Exercises""; ""6 Path integrals and holomorphic formalism""; ""6.1 Complex integrals and Wick�s theorem""; ""6.2 Holomorphic representation""; ""6.3 Kernel of operators""; ""6.4 Path integral: the harmonic oscillator""; ""6.5 Path integral: general hamiltonians""; ""6.6 Bosons: second quantization""
- ""6.7 Quantum statistical physics: the partition function""""6.8 Bose�Einstein condensation""; ""6.9 Generalized path integrals: the quantum Bose gas""; ""6.10 Partition function: the field integral representation""; ""Exercises""; ""7 Path integrals: fermions""; ""7.1 Grassmann algebras""; ""7.2 Differentiation in Grassmann algebras""; ""7.3 Integration in Grassmann algebras""; ""7.4 Gaussian integrals and perturbative expansion""; ""7.5 Fermion vector space and operators: one state""; ""7.6 General Grassmann analytic functions""; ""7.7 Many-fermion states. Hamiltonians""