Reference: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 1.17.

Here’s another example of calculating the uncertainty principle. We have a wave function defined as

The constant is determined by normalization in the usual way:

The expectation value of is from the symmetry of the wave function. The expectation value of is

[We can’t calculate in this case, because we know the value of only at one specific time (), so we don’t have enough information to calculate its derivative.]

The remaining statistics are (the integrals are all just integrals of polynomials, so nothing complicated):

Thus the uncertainty principle is satisfied in this case.

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ValcoHi there….

first of all, thanks for this amazing work. It is very helpful in my study.

About this exercise, equation 9 is wrong, a small copy-paste mistake, I think.

x^2 is missing at the integral.

Thanks

gwrowePost authorFixed now. Thanks.

shilpa ChakrabortyThanks