Error in the Time‐Dependent Perturbation Theory of Quantum Mechanics

1997 ◽  
Vol 10 (1) ◽  
pp. 40-49
Author(s):  
Zhang Junhao
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Time Dependent

A modification of the Dirac time-dependent perturbation theory

1984 ◽  
Vol 394 (1807) ◽  
pp. 345-361 ◽  
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Time Dependent ◽  
Static Case ◽  
Simple Route ◽  
Factors Associated ◽  
Perturbation Procedure ◽  
Variation Of Constants ◽  
Harmonic Perturbation ◽  
Secular Terms

Within the framework of the method of variation of constants, time-dependent perturbation theory is presented in a form that naturally eliminates the undesirable ‘secular ’ terms for a time-independent perturbation, permits an order-by-order calculation of the exact wavefunction for a ‘resonant’ harmonic perturbation and offers a simple route to establish the adiabatic hypothesis in quantum mechanics. The formulation rests on the introduction of a flexibility in the choice of the phase factors associated with the varying amplitudes, together with development of a perturbation procedure that closely resembles the Brillouin-Wigner formalism in the static case, and which exploits the flexibility of the phase factors at each order of the theory.

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