Exact solutions of ann-dimensional anisotropic oscillator in a uniform magnetic field

Autor:	E. E. Bergmann, A. Holz
Rok vydání:	1972
Předmět:	Physics Matrix (mathematics) symbols.namesake Quantum mechanics Gaussian function symbols Anisotropy Linear combination Hamiltonian (quantum mechanics) Harmonic oscillator Eigenvalues and eigenvectors Magnetic field Mathematical physics
Zdroj:	Il Nuovo Cimento B Series 11. 7:265-276
ISSN:	1826-9877
DOI:	10.1007/bf02743599
Popis:	A set of exact solutions is found from the positive-definite HamiltonianH=1/2(pM−1p + [q,Aq]+ +qKq), whereM andK are symmetric, realn xn matrices and whereA is an arbitrary realn xn matrix. This Hamiltonian corresponds to an anisotropic harmonic oscillator in a uniform magnetic field. The method consists of solving a 2n-dimensional eigenvalue problem. The eigenvalues provide the characteristic transition frequencies and the eigenvectors are used to construct annihilation and creation operatorsaj and aj+. The procedure is similar to Bogolyubov transformation. These eigenvectors are also used to re-express theq andp as linear combinations of theseaj and aj+. The ground-state function is found; in the appropriate gauge it is a real Gaussian function of theq.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7babbfeec7d90b67eb072ecc38137e06 https://doi.org/10.1007/bf02743599 Zobrazit plný text záznamu Full text from SpringerLink