StudentLearningDifficulties

StudentLearningDifficulties - PHYS 3220 - Quantum I Student...

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PHYS 3220 - Quantum I Student Learning Difficulties This document provides a brief summary of common student learning difficulties which have been previously published in studies of student learning in upper-division quantum mechanics. Because many of the documented difficulties fall into well defined categories such as time development, most of the difficulties are grouped into subject-specific tables. In these tables, the phrase, “some students say that …”, may also be read as “answers provided by some students are consistent with the believe that …”. Student learning difficulties related to time development in quantum mechanics Student Learning Difficulties: Time Development Students believe that if the system is initially in an eigenstate of an operator Ĝ, then the expectation value of that operator is time independent. Some students say that an eigenstate of any operator is a stationary state. Some students say that if the system is in an eigenstate of any operator Ĝ, then it remains in the eigenstate of Ĝ forever unless an external perturbation is applied. Some students say that if the time dependent exponential factors cancel out in the expectation value for an operator Ĝ, then the system (e.g., the wave function) does not evolve. Some students say that all allowable quantum states have a definite energy, even states which are superposition of energy eigenstates with different energies. An example of this type of statement is Ψ ( x , t ) = ( Ay 1 + By 2 )exp(- iEt /h) when ψ 1 and ψ 2 are energy eigenstates with different energies. Some students say that there is no relationship between the Hamiltonian operator and the time
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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.

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StudentLearningDifficulties - PHYS 3220 - Quantum I Student...

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