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Solving Problems Using Quantum Mechanics 
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#1
Nov2612, 05:05 PM

P: 142

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
Nov2612, 05:37 PM

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P: 11,896

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
Nov2612, 06:59 PM

P: 150

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.



#4
Nov2612, 07:25 PM

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PF Gold
P: 29,239

Solving Problems Using Quantum Mechanics
Zz. 


#5
Nov2612, 09:37 PM

Mentor
P: 16,195

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
Nov2712, 05:01 AM

P: 142

Can you give me some guidelines of the involving steps? 


#7
Nov2712, 05:56 AM

Mentor
P: 16,195

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
Nov2712, 06:05 AM

P: 1,020

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



#9
Nov2712, 01:09 PM

P: 142

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
Nov2712, 01:10 PM

P: 142




#11
Nov2712, 03:21 PM

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Thanks
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#12
Nov2812, 12:32 AM

P: 1,020



#13
Nov2812, 09:45 PM

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PF Gold
P: 2,063

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
Nov2912, 02:28 PM

P: 142

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?



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