Abstract
In upper level quantum mechanics courses, the typical process of devoting significant time to the example of a finite square potential well does not provide students with sufficient mastery of the relevant physics concepts and mathematical techniques to solve new problems.
Highlights
Bound and scattering states are two fundamental concepts in quantum mechanics
The results showed that many students confuse the bound and scattering states and have difficulty reasoning about the corresponding physical properties
The boundary state problem in exams explicitly provides an expression of the one-dimensional potential VðxÞ, which could prompt students to activate tools to solve the corresponding ordinary differential equations
Summary
Bound and scattering states are two fundamental concepts in quantum mechanics. When the energy of a particle is less than the potential energy at infinity, the particle is in a bound state. Otherwise, it is in a scattering state. Different shapes between the bound and scattering state wave functions give rise to measurable differences in the experimental results. As a case where quantum mechanics is very different from classical mechanics and has a wide range of applications, the quantum tunneling effect and associated scattering states are an important part of any quantum mechanics course. A solid understanding of the bound and scattering states is a key element in mastering the fundamental content of quantum mechanics
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