I have a particle of mass m in a box of length L. The energy eigenstates of this particle have wave functions(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\phi_{n}(x)=\sqrt{2/L}sin(n \pi x/L)[/tex]

and energies

[tex]E_n = n^{2}\pi^{2}\hbar^{2}/2mL^{2}[/tex]

where n=1, 2, 3,... At time t=0, the particle is in a state described as follows.

[tex]\Psi(t=0)=\frac{1}{\sqrt{14}}[\phi_1 + 2\phi_2 + 3\phi_3][/tex]

To find the energy for state [tex]\Psi[/tex] I did the following.

[tex]\sum_{1, 2, 3} E_n = (1^2 + 2^2 +3^2) \frac{\pi^2\hbar^2}{2mL^2}=14\frac{\pi^2\hbar^2}{2mL^2}= 14E_1 [/tex]

where [tex]E_1=\frac{\pi^2\hbar^2}{2mL^2}[/tex]

I have made a mistake somewhere because the actual answer is [tex]9 E_1[/tex]. Does anyone know where my error is?

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# Homework Help: Energy Eigenstates

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