Spiked harmonic oscillators
نویسندگان
چکیده
منابع مشابه
Spiked Harmonic Oscillators
A complete variational treatment is provided for a family of spiked-harmonic oscillator Hamiltonians H = − d dx2 + Bx + λ x (B > 0, λ > 0 ), for arbitrary α > 0 . A compact topological proof is presented that the set S = {ψn} of known exact solutions for α = 2 constitutes an orthonormal basis of the Hilbert space L2(0,∞) . Closed-form expressions are derived for the matrix elements of H with re...
متن کاملExact solutions for a family of discretely spiked harmonic oscillators
5 Normalization and orthogonalization 15 5.1 Admissible physical solutions . . . . . . . . . . . . . . . . . . 16 5.2 Linear normalization . . . . . . . . . . . . . . . . . . . . . . . 16 5.3 Radial normalization . . . . . . . . . . . . . . . . . . . . . . . 18 5.3.1 One dimensional . . . . . . . . . . . . . . . . . . . . . 18 5.3.2 Two dimensional . . . . . . . . . . . . . . . . . . . . . 20 5...
متن کاملSpiked harmonic quantum toboggans
Quantum particle is assumed located in an analytically perturbed harmonic-oscillator potential. Its motion along certain complex, PT −symmetric “toboggan” paths which N−times encircle the branch point in the origin is studied in both the boundstate and scattering regime.
متن کاملGeneralized Spiked Harmonic Oscillator
A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = − d dx + Bx + A x + λ xα ,where B > 0, A ≥ 0 , and α and λ denote two real positive parameters. The method makes use of the function space spanned by the solutions |n> of Schrödinger’s equation for the potential V (x) = Bx + A x . Compact closed-form expressions are obtai...
متن کاملCoupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerf...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2002
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1418247