Why Is My Calculation of the Particle Energy in a Rectangular Box Different?

[cgw]

I am missing something.

The question is to find the 6 lowest energy states of a particle of mass m in a box with edge lengths of $$L_{1}=L$$, $$L_{2}=2L$$, $$L_{3}=2L$$.
The answer gives $$E_{0}=\frac{\pi^2\hbar^2}{8mL^2}$$.

I would have said $$E_{0}=\frac{3\pi^2\hbar^2}{4mL^2}$$ .

What am I missing?
(the answer given for the actual question is 6, 9, 9, 12, 14, 14)

 

[cgw]

Finally figured out the latex.

 

[Mentz114]

Well done with the latex. Why would you say what you say ?

I don't know what you mean by "6, 9, 9, 12, 14, 14".

 

[cgw]

The question asks for the energy of the six lowest states $$\frac{E}{E_{0}}$$. The textbook answer gives $$E_{0}=\frac{\pi^2\hbar^2}{8mL^2}$$

The way I see it is:

E = E_0 at n1=1, n2=1, n3=1


$$E_{0}=\frac{\pi^2\hbar^2}{2m}\left{\left(\frac{n_{1}}{L}\right)^2+\left(\frac{n_{2}}{2L}\right)^2+\left(\frac{n_{3}}{2L}\right)^2\right}$$

which should be $$E_{0}=\frac{3\pi^2\hbar^2}{4mL^2}$$