- #1
Hart
- 169
- 0
Homework Statement
Determing the constant c such that [tex]\psi_{c}(x,y,z) = x^{2}+cy^{2}[/tex] is an eigenfunction of [tex]\hat{L_{z}}[/tex]
Homework Equations
[tex]\hat{L_{z}} = -i \hbar (x\frac{\partial \psi}{\partial y} - y\frac{\partial \psi}{\partial x}[/tex]
The Attempt at a Solution
[tex]x\frac{\partial \psi}{\partial y} - y\frac{\partial \psi}{\partial x}) = 2x^{2}-2y^{2}c[/tex]
Therefore:
[tex]\hat{L_{z}} \psi = -i \hbar (2x^{2}-2y^{2}c) = -2i \hbar (x^{2}-y^{2}c)[/tex]
.. and now I'm stuck. :|