How Do I Solve These Quantum Mechanics Problems from Binney's Textbook?

[pierce15]

Homework Statement

http://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf[/PLAIN]

page 42 in pdf (34 in the book)

problems 2.3, 2.5, 2.8, 2.9 (there are more but I'll start with these)

Homework Equations

I'll just include these for particular problems

The Attempt at a Solution

2.3

a. $\langle \psi | Q | \psi \rangle$ is the expected value of Q in the quantum state $| \psi \rangle$; $| \langle q_n | \psi \rangle | ^2$ - probability of $q_n$ occurring in state $| \psi \rangle$

b. the first operator is the identity operator, the second is the "observable" operator (bad phrasing?)

c. $u_n (x) = \langle x | q_n \rangle$, so $\langle q_n | \psi \rangle = u_n^*(\psi)$; I'm not really sure where to go from there
2.5

a. $\langle x \rangle = \langle \psi | \hat{x} | \psi \rangle$

b. $\langle x^2 \rangle = \langle \psi | \hat{x}^2 | \psi \rangle$

c. $\langle p_x \rangle = \langle \psi | \hat{p} | \psi \rangle$

I won't bother writing down the last one because I'm pretty sure those are wrong anyway2.8- i don't know where to start with this problem, sorry2.9

Ehrenfest's theorem:

$$ i \hbar \frac{d}{dt} \langle \psi | Q | \psi \rangle = \langle \psi | [ Q, H ] | \psi \rangle + i \hbar \langle \psi | \frac{dQ}{dt} | \psi \rangle $$

I'm not sure where to go from there.

Any help would be greatly appreciated.

 

[jedishrfu]

I would suggest devoting one thread per problem rather than trying to discuss all of them at once.

You also need to show more work. We can't do your homework here but we can't help get you out of a bind so do a little more research and show more work.