enter image description hereOur teacher gave us a question for exercise. I tried but I couldn't solve it. Please help me solve this problem. This section come after infinite square well on the griffits introduction quantum mechanics. step potantial is not included.

The state of a particle of mass m in the harmonic oscillator potential at $t = 0$ is

$$\psi(x,0)=\ (\frac{1}{\sqrt{5}})\psi_1(x)+ (\frac{2}{\sqrt{5}})\psi_2(x).$$

What is the expectation value of energy?


closed as off-topic by DanielSank, FGSUZ, ZeroTheHero, G. Smith, M. Enns Jan 12 at 1:20

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    $\begingroup$ You're going to have to show us what you tried so we have some basis for how to formulate our responses to you. Otherwise we don't know what specifically you are having an issue with. $\endgroup$ – Triatticus Jan 11 at 22:25
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    $\begingroup$ I don't think homework questions are appropriate for this particular site. There is a tag for homework if you want that addressed. Also, we don't directly answer homework but if there is a principle of physics that needs clarifying and this is clear in the question it is appropriate. $\endgroup$ – ggcg Jan 11 at 22:26
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    $\begingroup$ If you were given this type of problem then I would think by now you have had (1) linearity of the operators, and (2) the definition of the expectation value of a q-variable. These 2 concepts are enough to proceed. $\endgroup$ – ggcg Jan 11 at 22:27
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    $\begingroup$ Please replace the statement that you "tried hard" with actual text showing what you tried and where you got stuck. $\endgroup$ – DanielSank Jan 11 at 23:17
  • $\begingroup$ Hint: what are the probabilities and eigenenergies of the $\psi_1$ and $\psi_2$ states? $\endgroup$ – J.G. Jan 12 at 18:16