Renormalizing the kinetic energy operator in elementary quantum mechanics
In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an...
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| Veröffentlicht in: | European journal of physics 2009-09, Vol.30 (5), p.1015-1023 |
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| creator | Coutinho, F A B Amaku, M |
| description | In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness. |
| doi_str_mv | 10.1088/0143-0807/30/5/010 |
| format | Article |
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| ispartof | European journal of physics, 2009-09, Vol.30 (5), p.1015-1023 |
| issn | 0143-0807 1361-6404 |
| language | eng |
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| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | College Science Communication, education, history, and philosophy Energy Equations (Mathematics) Exact sciences and technology General physics Kinetics Physics Physics literature and publications Problem Solving Quantum Mechanics Science Instruction Scientific Principles Surveys and tutorial papers, resource letters |
| title | Renormalizing the kinetic energy operator in elementary quantum mechanics |
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