Energy spectrum of the long-range Lennard-Jones potential

• URL: http://arxiv.org/abs/2502.12271v1
• Date: Mon, 17 Feb 2025 19:15:56 GMT
• Title: Energy spectrum of the long-range Lennard-Jones potential
• Authors: Shahar Hod,
• Abstract summary: We study the discrete energy spectra of inverse power-law binding potentials of the form $V(r;alpha,beta,n)=-alpha/r2+beta/rn$ with $n>2$. Our results are of practical importance for the physics of polarized molecules, the physics of composite polymers, and also for physical models describing the quantum interactions of bosonic particles.
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• Abstract: The discrete energy spectra of composite inverse power-law binding potentials of the form $V(r;\alpha,\beta,n)=-\alpha/r^2+\beta/r^n$ with $n>2$ are studied {\it analytically}. In particular, using a functional matching procedure for the eigenfunctions of the radial Schr\"odinger equation, we derive a remarkably compact analytical formula for the discrete spectra of binding energies $\{E(\alpha,\beta,n;k)\}^{k=\infty}_{k=1}$ which characterize the highly-excited bound-state resonances of these long-range binding potentials. Our results are of practical importance for the physics of polarized molecules, the physics of composite polymers, and also for physical models describing the quantum interactions of bosonic particles.

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