1
$\begingroup$

I read another Phys.SE post here: 3D Quantum harmonic oscillator that I believe says the wave function in Cartesian coordinates for a 3D harmonic oscillator is the product of the 3 one dimensional wave functions. If so, are the angular and radial equations combined within it? Is it possible to separate the radial part from the angular part?

The wavefunction for 1D in the ground state is $$\psi_{0}(x)=(\frac{m\omega}{\pi\hbar})^{\frac{1}{4}}e^{-\frac{m\omega x^{2}}{2\hbar}}.$$

I think this product would then be: $$\psi_{0}(r)=(\frac{m\omega}{\pi\hbar})^{\frac{3}{4}}e^{-\frac{m\omega r^{2}}{2\hbar}}.$$

Is this the radial equation for the ground state? Would I then need to multiply by the angular equation for the ground state to get the full wave equation?

$\endgroup$
1
$\begingroup$

You can definitely represent a 3d QHO wavefunction as a composition of radial components and angular components (spherical harmonics).

$\endgroup$
  • 1
    $\begingroup$ @curiousGeorge119 : See Wiki $\endgroup$ – Trimok Dec 9 '13 at 20:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.