**Required math: calculus **

**Required physics: **Schrödinger equation

Reference: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 2.4.

We can calculate the mean values of position and momentum and verify the uncertainty principle for the infinite square well. The Schrödinger equation for the square well is, between and :

The stationary states of the infinite square well are given by

for .

For we have

For the momentum we have

The uncertainty principle here is then:

The smallest uncertainty will be for the state and is approximately , which satisfies the condition .

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rituparna ghoshwhere is the constant Cn in the expression of shai (wave function)

gwrowePost authorI don’t understand your question. What constant Cn are you referring to?

rituparna ghoshsorry it’s my mistake, actually I was confusing between the stationary state and linear combination of them! my mistake! sorry

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alokGriffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 2.4 . Could you help me with the solution of , i am not getting “a/2”?

Mike RandleIt took me around an hour of confusion to realize that the oscillating terms reduce. Specifically, sin(2*pi*n) and cos(2*pi*n) become 0 and 1 respectively because n is defined only by integers. Once the oscillating terms reduce, you recover Griffith’s solution. It is just one of those things that I had never encountered before. If n were defined on the reals instead of integers, this simplification would not happen.