dorsal/arxiv
View SchemaSum rules for Confining Potentials
| Authors | C. V. Sukumar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611066 |
| URL | https://arxiv.org/abs/quant-ph/0611066 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Using the Green's function associated with the one-dimensional Schroedinger equation it is possible to establish a hierarchy of sum rules involving the eigenvalues of confining potentials which have only a boundstate spectrum. For some potentials the sum rules could lead to divergences. It is shown that when this happens it is possible to examine the separate sum rules satisfied by the even and odd eigenstates of a symmetric confining potential and by subtraction cancel the divergences exactly and produce a new sum rule which is free of divergences. The procedure is illustrated by considering symmetric power law potentials and the use of several examples. One of the examples considered shows that the zeros of the Airy function and its derivative obey a sum rule and this sum rule is verified. It is also shown how the procedure may be generalised to establish sum rules for arbitrary symmetric confining potentials.
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"abstract": "Using the Green\u0027s function associated with the one-dimensional Schroedinger\nequation it is possible to establish a hierarchy of sum rules involving the\neigenvalues of confining potentials which have only a boundstate spectrum. For\nsome potentials the sum rules could lead to divergences. It is shown that when\nthis happens it is possible to examine the separate sum rules satisfied by the\neven and odd eigenstates of a symmetric confining potential and by subtraction\ncancel the divergences exactly and produce a new sum rule which is free of\ndivergences. The procedure is illustrated by considering symmetric power law\npotentials and the use of several examples. One of the examples considered\nshows that the zeros of the Airy function and its derivative obey a sum rule\nand this sum rule is verified. It is also shown how the procedure may be\ngeneralised to establish sum rules for arbitrary symmetric confining\npotentials.",
"arxiv_id": "quant-ph/0611066",
"authors": [
"C. V. Sukumar"
],
"categories": [
"quant-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Sum rules for Confining Potentials",
"url": "https://arxiv.org/abs/quant-ph/0611066"
},
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