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Considering a particle in 3d, the corresponding Hilbert space $H$ is the tensor product of individual Hilbert spaces

$H=(H_x \otimes H_y \otimes H_z)$

If the particle is in a potential $V(x,y,z)$ ,what is the corresponding potential operator for it?

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If $V(x,y,z)$ has a development as a series in $x,y,z$, then the potential operator $\hat V$ is obtained by replacing $x,y,z$ in the series by the corresponding operators $\hat x \otimes 1 \otimes 1, 1\otimes \hat y \otimes 1$ and $1\otimes 1 \otimes \hat z$.

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  • $\begingroup$ $f (x, y) = f (a, b) + f_x(a, b) (x - a) $ what do I replace f(a,b) by? $\endgroup$
    – Kashmiri
    Mar 18 at 6:16
  • $\begingroup$ This constant times the identity operator. $\endgroup$ Mar 18 at 8:45
  • $\begingroup$ Thank you...... $\endgroup$
    – Kashmiri
    Mar 18 at 8:52

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