Question

*Problem 1.9

Answer 1

what can we say about the result..
\[\sigma_x\sigma_p=\sqrt{\frac \hbar {4am}}\sqrt{am\hbar}=\frac \hbar2\]

Answer 2

It fits the the Heisenberg uncertainty principle.

Answer 3

only just

Answer 4

ONLY just yes. I guess that's the point.

Answer 5

That's right, in general a Gaussian is the closest you can come to violating the uncertainty principle but as is shown, it still fits.

Answer 6

The first part of the question can be solved by normalization the function i.e we know that \[\int\limits_{a}^{b}\Psi \times \Psi*=1\]
Wherwe can just square the function and then integrate it from -infi to +infi and then equation it to 1

Answer 7

1.9.pdf is my solutions @punnus