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On the new approach to variable separation in the time-dependent Schrödinger equation with two space dimensions (1995)

Zhdanov, R. Z. ; Revenko, I. V. ; Fushchych, W. I.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 36 (1995), S. 5506-5521

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: We suggest an effective approach to separation of variables in the Schrödinger equation with two space variables. Using it we classify inequivalent potentials V(x1,x2) such that the corresponding Schrödinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schrödinger equation with the anisotropic harmonic oscillator potential V=k1x21+k2x22 and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schrödinger equation (V=0). © 1995 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.531274

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