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This investigation reveals the relationship between well depth and tunneling in quantum particles, indicating implications for uncertainty principles.
We investigate the problem of a quantum particle confined in a finite one-dimensional square well. The eigenvalues and eigenfunctions are found using a computer algebra system to solve the equations that result from matching the logarithmic derivatives at the well boundaries. The wavefunctions are used to investigate the relation of well depth to tunneling and to the Heisenberg uncertainty relations. We demonstrate how dimensional analysis can be used to locate the minimum uncertainty for a given confining potential.
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Blank et al. (2010) studied this question.
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