scholarly journals Investigating student understanding of basic quantum mechanics in the context of time-dependent perturbation theory

2014 ◽  
Author(s):  
Gina Passante ◽  
Paul J. Emigh ◽  
Peter S. Shaffer
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Student Understanding ◽  
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.

scholarly journals A measurement of quantum fears

2016 ◽  
pp. 66-76
Author(s):  
JR Chapman ◽  
SO Hunt ◽  
NR Walet
Keyword(s):  
Quantum Mechanics ◽  
Time Dependence ◽  
Student Understanding ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Threshold Concepts ◽  
Survey Analysis ◽  
Student Difficulties ◽  
Self Evaluation

There are anecdotal indications that students avoid questions involving time-dependent exam problems in quantum mechanics. To obtain real evidence, a diagnostic questionnaire has been created and administered to third-year students. It measures students' understanding of quantum mechanics in general, with an emphasis on misconceptions and threshold concepts that may block a deeper under-standing of quantum mechanics, especially of time-dependent aspects. The questionnaire consists of two parts, a self-evaluation section followed by a conceptual survey. Analysis of the results of this questionnaire does indeed reveal areas of weakness in student understanding of time-dependence as well as of other fundamental quantum mechanical concepts. The questionnaire has been revised in light of the analysis with the aim of improving the understanding of student difficulties as well as the reliability of the questionnaire itself.

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