Hwasung Lee and Y J Lee 2007 J. Phys. A: Math. Theor. 40 3569 doi:10.1088/1751-8113/40/13/017
Determinable solutions for one-dimensional quantum potentials: scattering, quasi-bound and bound-state problems
Hwasung Lee1,3 and Y J Lee2
Show affiliationsWe derive analytic expressions of the recursive solutions to Schrödinger's equation by means of a cutoff-potential technique for one-dimensional piecewise-constant potentials. These solutions provide a method for accurately determining the transmission probabilities as well as the wavefunction in both classically accessible regions and inaccessible regions for any barrier potentials. It is also shown that the energy eigenvalues and the wavefunctions of bound states can be obtained for potential-well structures by exploiting this method. Calculational results of illustrative examples are shown in order to verify this method for treating barrier and potential-well problems.
- PACS
- MSC
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81Uxx Scattering theory (See also 34A55, 34L25, 34L40, 35P25, 47A40)
- Subjects
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Surfaces, interfaces and thin films
- Dates
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Issue 13 (30 March 2007)
Received 21 November 2006, in final form 8 January 2007
Published 14 March 2007
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Determinable solutions for one-dimensional quantum potentials: scattering, quasi-bound and bound-state problems
Hwasung Lee and Y J Lee 2007 J. Phys. A: Math. Theor. 40 3569
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