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ON SOLVING THE SCHRÖDINGER-LIKE WAVE EQUATION IN N DIMENSIONS FOR GENERALIZED SEXTIC AND OCTIC POTENTIALS

R. S. Kaushal

Open publisher page 8 citations

Abstract

For a potential of the type [Formula: see text], where n=6, 8, we obtain an exact analytic solution of the Schrödinger-like wave equation generalized to N dimensions. We make use of an ansatz for the eigenfunction and obtain a closed form expression for the energy eigenvalues at the cost of certain constraints on the potential parameters, bk. A distinct feature for even power potentials is pointed out for the case b0=0.

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What this paper is about

For a potential of the type [Formula: see text], where n=6, 8, we obtain an exact analytic solution of the Schrödinger-like wave equation generalized to N dimensions. We make use of an ansatz for the eigenfunction and obtain a closed form expression for the energy eigenvalues at the cost of certain constraints on the potential parameters, bk. A distinct feature for even power potentials is pointed out for the case b0=0.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

For a potential of the type [Formula: see text], where n=6, 8, we obtain an exact analytic solution of the Schrödinger-like wave equation generalized to N dimensions. We make use of an ansatz for the eigenfunction and obtain a closed form expression for the energy eigenvalues at the cost of certain constraints on the potential parameters, bk. A distinct feature for even power potentials is pointed out for the case b0=0.

Key concepts: Eigenfunction, Physics, Ansatz, Eigenvalues and eigenvectors, Schrödinger equation, Mathematical physics, Wave function, Mathematical analysis

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ON SOLVING THE SCHRÖDINGER-LIKE WAVE EQUATION IN N DIMENSIONS FOR GENERALIZED SEXTIC AND OCTIC POTENTIALS — Research Paper | ScholarLens