Transformation properties of wave functions of a two-dimensional harmonic oscillator

A transformation formula for wave functions of type $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}$$ , where ψn is the eigenfunction of a harmonic oscillator for the nth energy level, was found for an arbitrary rotation of the (x 1, x 2) Cartesian system. By way of example, matrix elements for contact interaction of two particles in an external harmonic potential field were calculated.

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