PATH INTEGRALS WITH PERIODIC CONSTRAINTS. 1. QUANTUM MECHANICS OF A PARTICLE ON A RING

H. O. Girotti, T. J. M. Simões

Jean Zinn‐Justin

Luiz C. L. Botelho

We show that Nelson's stochastic mechanics suitably formulated as a Hamilton–Jacobi first-order equation leads straightforwardly to the Feynman path integral formulation of quantum mechanics.

Rainer Dick

Fiorenzo Bastianelli A, Peter van Nieuwenhuizen

Jean Zinn‐Justin

1. Gaussian integrals 2. Path integral in quantum mechanics 3. Partition function and spectrum 4. Classical and quantum statistical physics 5. Path integrals and quantization 6. Path integral and holomorphic formalism 7. Path integrals: fermions 8. Barrier penetration: semi-classical approximation 9. Quantum evolution and scattering matrix 10. Path integrals in phase space QUANTUM MECHANICS: MINIMAL BACKGROUND A1 Hilbert space and operators A2 Quantum evolution, symmetries and density matrix A3 Position and momentum. Scrodinger equation