On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models
Among P-pseudo-Hermitian Hamiltonians H = P⁻¹H†P with real spectra, the ''weakly pseudo-Hermitian'' ones (i.e., those employing non-self-adjoint P ≠ P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P ≠...
Збережено в:
| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148972 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Цитувати: | On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 25 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148972 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1489722019-02-20T01:25:25Z On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models Znojil, M. Among P-pseudo-Hermitian Hamiltonians H = P⁻¹H†P with real spectra, the ''weakly pseudo-Hermitian'' ones (i.e., those employing non-self-adjoint P ≠ P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P ≠ P†, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasiparity operator Q. We show how, in this language, the standard quantum mechanics is restored via the two alternative inner products in the physical Hilbert space of states, with <ψ₁|PQ|ψ₂> = <ψ1|CP|ψ2>. 2008 Article On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 25 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81Q10; 47B50 http://dspace.nbuv.gov.ua/handle/123456789/148972 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Among P-pseudo-Hermitian Hamiltonians H = P⁻¹H†P with real spectra, the ''weakly pseudo-Hermitian'' ones (i.e., those employing non-self-adjoint P ≠ P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P ≠ P†, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasiparity operator Q. We show how, in this language, the standard quantum mechanics is restored via the two alternative inner products in the physical Hilbert space of states, with <ψ₁|PQ|ψ₂> = <ψ1|CP|ψ2>. |
| format |
Article |
| author |
Znojil, M. |
| spellingShingle |
Znojil, M. On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Znojil, M. |
| author_sort |
Znojil, M. |
| title |
On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_short |
On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_full |
On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_fullStr |
On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_full_unstemmed |
On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models |
| title_sort |
on the role of the normalization factors κn and of the pseudo-metric p ≠ p† in crypto-hermitian quantum models |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148972 |
| citation_txt |
On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 25 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT znojilm ontheroleofthenormalizationfactorsknandofthepseudometricppincryptohermitianquantummodels |
| first_indexed |
2023-05-20T17:31:55Z |
| last_indexed |
2023-05-20T17:31:55Z |
| _version_ |
1796153516826296320 |