Recent content by timn

Much clearer! Looking at the momentum makes it more concrete. Thank you very much.

Thank you ardie, that makes it clearer.

Thanks vela! I forgot that the Hamiltonian is the energy operator. Much clearer now.

Matterwave, I'm learning on my own by reading Gasiorowicz's Quantum Physics, which I know is used for introductory QM courses. I'd love a suggestion for a way to find the answers to these standard questions without bothering the helpful people over here.

What is special about energy eigenstates? How could I know if an eigenstate of a quantity is such that the particle stays in it indefinitely? Also, are other eigenstates still called stationary states, even if they aren't stationary?

Homework Statement Solve the time-independent Schrödinger equation in one dimension for a potential step, i.e. V(x) = 0 for x<0 and V(x) = V_0 for x>0. Homework Equations - \frac{\hbar^2}{2m} \frac{d^2u(x)}{dx^2} + V(x)u(x) = Eu(x) The Attempt at a Solution Rewrite as (4-3)...

So since the state of the system is not a single eigenstate, but a superposition of at least two, it will change with time. Your answer made me a lot wiser -- thank you!

Future of a particle in a box -- I'm fundamentally confused Homework Statement A particle is somewhere in the right half of a one-dimensional infinite potential well with sides at x=-a/2 and x=a/2. The particle's wave function is constant over x, i.e. \psi(x) = \sqrt{2/a} for 0<x<a/2...

Thanks for your suggestions on the unit rearrangements, vela. I'll keep that in mind and see if it makes things easier. The answers were found in a shady .doc file from scribd, and this would not be the first error. Thanks!

Sorry about missing the 3 and the electron mass -- it's supposed to say 0.9*10^-30. I'll look through your calculations and simplifications soon. Thank you very much for the input!

Homework Statement Consider an electron of mass m=9*10^-30 kg in an infinite box of dimension a=10^-9 m. What is the energy difference between the ground state and the first excited state? Express your answer in eV. Homework Equations E_n = \frac{\hbar^2\pi^2n^2}{2ma^2} The Attempt at a...

Aha! I had forgotten about the orthogonality. Also, I had an epiphany when I realized that A_n = \int_0^a u_n^*(x) \psi(x) dx is just a projection. Thank you!

Homework Statement This is an example from Gasiorowicz's Quantum Physics. "Example 3-1" is a particle in an infinite potential-well, but that should not matter. Homework Equations The Attempt at a Solution Why is P(-2) (which I suppose is the probability that the eigenvalue -2 is...

The ion doesn't move there by itself, so the work required to push the ion is positive.

I see. I just assumed that SI units were used. Thank you!