# Solving Problems Using Quantum Mechanics

1. Nov 26, 2012

### 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.

2. Nov 26, 2012

### 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.

3. Nov 26, 2012

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. :yuck:

4. Nov 26, 2012

### ZapperZ

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

Zz.

5. Nov 26, 2012

Staff Emeritus
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.

6. Nov 27, 2012

### 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?

7. Nov 27, 2012

Staff Emeritus
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?

8. Nov 27, 2012

### andrien

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

9. Nov 27, 2012

### 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).

10. Nov 27, 2012

### bgq

What is wkb?

11. Nov 27, 2012

### Staff: Mentor

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

12. Nov 28, 2012

### andrien

13. Nov 28, 2012

### 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).

14. Nov 29, 2012

### 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?