Exploring Quantum Physics - Week 6 Question 8

Question:

What is the ground state energy of the potential $V\left(x_1,x_2,x_3\right)= \frac{M\omega^2}{2}\left(x_1^2+x_2^2+4x_3^2\right)$

Solution:

Following the same mindset in Question 4. The ground state energy is really just the sum of ground state energies, so that would be

$\hbar\omega\frac{1}{2} + \hbar\omega\frac{1}{2} + \hbar 2\omega\frac{1}{2} = 2\hbar\omega$.