Ground and excited states of spherically symmetric potentials through an imaginary-time evolution method: application to spiked harmonic oscillators

Starting from a time-dependent Schrödinger equation, stationary states of 3D central potentials are obtained. An imaginary-time evolution technique coupled with the minimization of energy expectation value, subject to the orthogonality constraint leads to ground and excited states. The desired diffu...

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Bibliographic Details
Published inJournal of mathematical chemistry Vol. 52; no. 10; pp. 2645 - 2662
Main Author Roy, Amlan K.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2014
Subjects
Chemistry
Chemistry and Materials Science
Math. Applications in Chemistry
Original Paper
Physical Chemistry
Theoretical and Computational Chemistry
Spherical symmetry
Imaginary-time evolution
Diffusion equation
Spiked oscillator
Time-dependent Schrodinger equation
Excited state
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Summary:Starting from a time-dependent Schrödinger equation, stationary states of 3D central potentials are obtained. An imaginary-time evolution technique coupled with the minimization of energy expectation value, subject to the orthogonality constraint leads to ground and excited states. The desired diffusion equation is solved by means of a finite-difference approach to produce accurate wave functions, energies, probability densities and other expectation values. Applications in case of 3D isotropic harmonic oscillator, Morse as well the spiked harmonic oscillator are made. Comparison with literature data reveals that this is able to produce high-quality and competitive results. The method could be useful for this and other similar potentials of interest in quantum mechanics. Future and outlook of the method is briefly discussed.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-014-0407-0