My question is given an orthonormal basis having the basis elements Ψ's ,matrix representation of an operator A will be [Ψ(adsbygoogle = window.adsbygoogle || []).push({}); _{i}IAIΨ_{j}] where i denotes the corresponding row and j the corresponding coloumn.

Similarly if given two dimensional harmonic oscillator potential operator .5kx^{2}+.5ky^{2}where x and y are the operators ,what will be the matrix representation of this operator in the 2d Cartesian basis where i and j are the unit vectors and this is an orthonormal basis??

What is the way to find these types of problems??

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# A Representing harmonic oscillator potential operator in. Cartesian basis

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