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2023•Physica ScriptaOpen access

Quantum infinite square well as a limiting case of higher order anharmonic oscillator

Y. Salamu

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Abstract

Abstract We present a new type of continuous anharmonic potential and analyze its higher order asymptotic limit. The potential display infinite square well-like behavior when anharmonic order N goes to infinity. Consequently, wave functions and eigenvalues of ground and first excited states of anharmonic oscillators also asymptotically approach to those of infinite square well.

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Abstract We present a new type of continuous anharmonic potential and analyze its higher order asymptotic limit. The potential display infinite square well-like behavior when anharmonic order N goes to infinity. Consequently, wave functions and eigenvalues of ground and first excited states of anharmonic oscillators also asymptotically approach to those of infinite square well.

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Available abstract

Abstract We present a new type of continuous anharmonic potential and analyze its higher order asymptotic limit. The potential display infinite square well-like behavior when anharmonic order N goes to infinity. Consequently, wave functions and eigenvalues of ground and first excited states of anharmonic oscillators also asymptotically approach to those of infinite square well.

Key concepts: Anharmonicity, Square (algebra), Particle in a box, Infinity, Physics, Limit (mathematics), Limiting, Eigenvalues and eigenvectors

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