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The approximate solution and the exact solution of three dimensional harmonic oscillator in potential H′=(λμω_0~2/2)(x~2+y~2+z~2)

Zhao Su-qin

The approximate solution and the exact solution of three dimensional harmonic oscillator in potential H′=(λμω_0~2/2)(x~2+y~2+z~2) is derived. The energy level and degeneracy of three dimensional harmonic oscillatorin in potential H′=(λμω_0~2/2)(x~2+y~2+z~2) is discussed.

jOURNAL OF southwest University for NationalitiesJan 1, 20070 citations

The Approximate Solution and the Exact Solution of Three Dimensional Harmonic Oscillator in Potential V=λxy

Zhao Su-qin

The Approximate Solution and the Exact Solution of three dimensional harmonic oscillator in Potential V=λxy is derived.The energy level and degeneracy of three dimensional harmonic oscillatorin in Potential V=λxy is discussed.

Journal of Qinghai Junior Teachers' CollegeJan 1, 20090 citations

The Change of Energy Levels and Degeneracy of Three Dimensional Harmonic Oscillator in the Uniform Magnetic Field

Zhao Su-qin

The formula of energy levels of three dimensional harmonic oscillator in the uniform magnetic field is derived.The lowest energy level and degeneracy is discussed.

Journal of Qinghai Normal UniversityJan 1, 20060 citations

ANALYTIC SOLUTION TO THE SCHRDINGER EQUATION WITH A HARMONIC OSCILLATOR POTENTIAL PLUS δ-POTENTIAL

Qinglin Peng

The analytic solution to the Schrodinger equation with a harmonic oscillator potentialplus δ-potential is presented in the coordinate representation. Its algebraic expression in theenergy representation is also given. The degeneracy of the energy levels is discussed and acomparison between the energy spectra of a harmonic oscillator and a particle in a δ-poten-tial is made.

Science China MathematicsJan 1, 19910 citations

Operators for the two-dimensional harmonic oscillator in an angular momentum basis

Olúwolé Òdúndún

The forms of the operators ν°, ν, λ°, λ, which enable one to write the Hamiltonian of the two-dimensional isotropic harmonic oscillator in the form H=ℏω(2ν°ν+λ°⋅λ+1), are presented. Here ν° and ν are, respectively, the raising and lowering operators for ν°ν, the ‘‘radial’’ quantum number operator, while λ° and λ are, respectively, the raising and lowering operators for M, the magnitude of the angular momentum operator. Corresponding to this decomposition of H in the angular momentum basis are the energy eigenvalues Ekm=ℏω(2k+‖m‖+1) with k=0, 1, 2, ⋅⋅⋅ and m=0, ±1, ±2, ⋅⋅⋅. Here k is a ‘‘radial’’ quantum number, and m is a ‘‘magnetic’’ quantum number. The commutation relations satisfied by the operators ν°, ν, λ°, and λ are also presented.The forms of the operators ν°, ν, λ°, λ, which enable one to write the Hamiltonian of the two-dimensional isotropic harmonic oscillator in the form H=ℏω(2ν°ν+λ°⋅λ+1), are presented. Here ν° and ν are, respectively, the raising and lowering operators for ν°ν, the ‘‘radial’’ quantum number operator, while λ° and λ are, respectively, the raising and lowering operators for M, the magnitude of the angular momentum operator. Corresponding to this decomposition of H in the angular momentum basis are the energy eigenvalues Ekm=ℏω(2k+‖m‖+1) with k=0, 1, 2, ⋅⋅⋅ and m=0, ±1, ±2, ⋅⋅⋅. Here k is a ‘‘radial’’ quantum number, and m is a ‘‘magnetic’’ quantum number. The commutation relations satisfied by the operators ν°, ν, λ°, and λ are also presented.

Journal of Mathematical PhysicsSep 1, 19832 citations

The Removal of Degeneracy of n=4 Energy Levels of Three Dimensional Harmonic Oscillatorin the Uniform Magnetic Field

Zhao Su-qin

The B2 proportional term in the Hamiltonian of three dimensional harmonic oscillator in the uniform magnetic field is considered,and calculated the perturbaion matrix elements.The complete removal of degeneracy of n=5 energy levels is discussed.

Journal of Qinghai Junior Teachers' CollegeJan 1, 20060 citations

The Solution of Two Dimensional Harmonic Oscillator in Potential H′=(λμω_0~2)/2(x~2+y~2)

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The Solution of Two Dimensional Harmonic Oscillator in Potential H′=(λμω_0~2)/2(x~2+y~2)

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