复旦量子力学讲义——qm2_chapter4课件.ppt

Chapter 4Path Integral §4.1 Classical action and the amplitude in Quantum Mechanics Introduction: how to quantize? Wave mechanics h ? Schr?dinger equ. Matrix mechanics h ? commutator Classical Poisson bracket ? Q. P. B. Path integral h ? wave function §4.1 Classical action and the amplitude in Quantum Mechanics Basic idea Infinite orbits Different orbits have different probabilities §4.1 Classical action and the amplitude in Quantum Mechanics A particle starting from a certain initial state may reach the final state through different possible orbits with different probabilities §4.1 Classical action and the amplitude in Quantum Mechanics Classical action §4.1 Classical action and the amplitude in Quantum Mechanics §4.1 Classical action and the amplitude in Quantum Mechanics §4.1 Classical action and the amplitude in Quantum Mechanics §4.1 Classical action and the amplitude in Quantum Mechanics Free particle §4.1 Classical action and the amplitude in Quantum Mechanics §4.1 Classical action and the amplitude in Quantum Mechanics Linear oscillator §4.1 Classical action and the amplitude in Quantum Mechanics §4.1 Classical action and the amplitude in Quantum Mechanics §4.1 Classical action and the amplitude in Quantum Mechanics §4.1 Classical action and the amplitude in Quantum Mechanics Amplitude in quantum mechanics All paths, not only just one path from a to b, have contributions The contributions of all paths to probability amplitude are the same in module, but different in phases The contribution of the phase from each path is proportional to S/h, where S is the action of the corresponding path §4.1 Classical action and the amplitude in Quantum Mechanics In summary: the quantization scheme of the path integral supposes that the probability P(a, b) of the transition is §4.1 Classical action and the amplitude in Quantum Mechanics §4.1 Classical action and the amplitude in Quantum Mechanics h appears as a part of the phase factor Q.M. ? C.M