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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In supersymmetric quantum mechanics, shape invariance is a sufficientcondition for solvability. We show that all conventional additive shapeinvariant superpotentials that are independent of $\hbar$ obey two partialdifferential equations. One of these is equivalent to the one-dimensional Eulerequation expressing momentum conservation for inviscid fluid flow, and it isclosed by the other. We solve these equations, generate the set of allconventional shape invariant superpotentials, and show that there are no othersin this category. We then develop an algorithm for generating all additiveshape invariant superpotentials including those that depend on $\hbar$explicitly.

Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation