English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the exactly solvable quantum system of two particles confined in athree-dimensional harmonic trap and interacting via finite-range soft-coreinteraction by means of the separation of variables and ansatz method.Supposing the solution in the form of ansatz $\Psi(r)=r^{a}e^{-\lambda r^2}\psi(r)$ we transform the time independent Schr\"{o}dinger equation intoKummer's differential equation whose solution are given in the form ofconfluent hypergeometric function. We also discuss that in the absence ofcentral force potential, the quantum system map into the problem of two quantumparticle trapped in one-dimension harmonic oscillator and interacting throughfinite distance soft-core potential. In such special case the eigen valueequation become the Weber's differential equation and its solution are alsogiven in the form of confluent hypergeometric function.

Two quantum particles trapped in three dimensions harmonic oscillator and interacting via finite range soft-core interaction