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As we know, the 1d infinite potential well has a stationary state. The function that depends on x onky is a sin function.

However, I don't understand the concept in this question. I have the answer of this question and this is not a homework. I am not asking for the answer so please don't put this post to the homework section.

I don't understand the part 2 of this question because the potential well should be in stationary state. Why i need to prove it in part 2?

Also, in part 3, i don't understand why there is a constant function. The fuction should be a product of sin function and exponential function. How come there is a constant function?

Thank you for your help