Solving Problems Using Quantum Mechanics

bgq

Hi,

I understand the basic principles of quantum mechanics, but I can't understand how to solve a practical problem using it. For example: Consider a stone of mass m = 2 Kg released from rest at height H=20m above the ground where friction is neglected; what is the speed of the stone when it reaches the ground? How we can solve such problem using quantum mechanics?

Thanks for any replies.

dextercioby

Essentially we can't. We can only use quantum mechanics where the concepts + postulates + theorems of it work. You can't expect to solve Atwood machines with Schrödinger's or Dirac's equation.

Dead Boss

It's not just a problem of applicability of equations. Have you tried solving Schrodinger equation for that problem? It's ridiculous compared to the simple classical solution.

ZapperZ

Is solving for the hydrogen energy level not a "practical problem"?

Zz.

Vanadium 50

This is not that hard a problem to solve with QM - it requires time dependent perturbation theory and a LOT of numerical integration. It's not a hard problem, but it is a very, very LONG problem.

It's also pointless, as the classical approach gives the right answer.

bgq

I can't find how can we use ψ function to find speed. It just gives probabilities and expected values for the position. How can we use it to find the speed at a certain point (like the proposed problem)?

Can you give me some guidelines of the involving steps?

Vanadium 50

Do you know how to do time dependent perturbation theory? Then you get the wavefunction as a function of time, and can calculate its mean position as a function of time. x(t) is what you want, right?

andrien

yes,you can find the energy by using wkb approximation,if particle is confined to above Z=0 by a perfectly reflecting plane?

bgq

I really do not know about time dependent perturbation theory; however, I am not looking for details but I try to understand - in general - how QM is applied in macroscopic world.
For the x(t) is only the mean position which may be not the position when reaching the ground; actually, I want v(x), so I can find the speed as v(H).

bgq

What is wkb?

Nugatory

It's a numerical approximation method discovered by Wentzel, Kramers, and Brillouin.

andrien

http://en.wikipedia.org/wiki/WKB_approximation

marcusl

Is there a reason you are trying to solve a macroscopic classical problem with quantum mechanics? QM is better for microscopic problems where classical physics cannot give answers (like the hydrogen atom that ZapperZ mentioned).

bgq

Thank you all for your replies. I just still have one question: Is Newton's 2nd Law valid in the quantum world? Can we use it to find in which quantum state will the system be?