Sum rules for odd and even states of confining potentials
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...
| Autore principale: | |
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| Natura: | Working paper |
| Pubblicazione: |
2018
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| _version_ | 1826269260708577280 |
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| author | Sukumar, C |
| author_facet | Sukumar, C |
| author_sort | Sukumar, C |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T21:22:18Z |
| format | Working paper |
| id | oxford-uuid:41ddc4bf-0dd2-4a54-905f-08687b103d59 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:22:18Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | oxford-uuid:41ddc4bf-0dd2-4a54-905f-08687b103d592022-03-26T14:46:13ZSum rules for odd and even states of confining potentialsWorking paperhttp://purl.org/coar/resource_type/c_8042uuid:41ddc4bf-0dd2-4a54-905f-08687b103d59Symplectic Elements at Oxford2018Sukumar, CUsing 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. |
| spellingShingle | Sukumar, C Sum rules for odd and even states of confining potentials |
| title | Sum rules for odd and even states of confining
potentials |
| title_full | Sum rules for odd and even states of confining
potentials |
| title_fullStr | Sum rules for odd and even states of confining
potentials |
| title_full_unstemmed | Sum rules for odd and even states of confining
potentials |
| title_short | Sum rules for odd and even states of confining
potentials |
| title_sort | sum rules for odd and even states of confining potentials |
| work_keys_str_mv | AT sukumarc sumrulesforoddandevenstatesofconfiningpotentials |