Solving Problems Using Quantum Mechanics

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Discussion Overview

The discussion revolves around the application of quantum mechanics to a classical problem involving a stone falling from a height. Participants explore whether quantum mechanics can be used to solve this problem and discuss the practicality and implications of such an approach.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions how to apply quantum mechanics to a classical problem of a stone falling, seeking guidance on the methodology.
  • Another participant argues that quantum mechanics is not applicable to such classical scenarios, suggesting that the classical solution is sufficient.
  • Some participants note that solving the Schrödinger equation for this problem would be impractical compared to classical methods.
  • There is mention of using time-dependent perturbation theory and numerical integration as potential methods within quantum mechanics, though some express skepticism about their utility for this problem.
  • One participant raises the idea of using the WKB approximation for energy calculations in a quantum context, questioning its relevance to the original problem.
  • Concerns are expressed about the validity of Newton's second law in quantum mechanics and its applicability to determining quantum states.

Areas of Agreement / Disagreement

Participants generally disagree on the applicability of quantum mechanics to the problem presented. While some suggest that quantum mechanics can be applied with complex methods, others maintain that it is unnecessary and impractical for a classical problem.

Contextual Notes

Participants highlight the limitations of applying quantum mechanics to macroscopic problems, emphasizing the differences in applicability between classical and quantum physics. There is also uncertainty regarding the interpretation of results from quantum mechanics in the context of classical scenarios.

Who May Find This Useful

This discussion may be of interest to those exploring the boundaries between classical and quantum mechanics, particularly in understanding the applicability of quantum theories to macroscopic phenomena.

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

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

Zz.
 
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.
 
Vanadium 50 said:
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.

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?
 
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?
 
yes,you can find the energy by using wkb approximation,if particle is confined to above Z=0 by a perfectly reflecting plane?
 
Vanadium 50 said:
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?

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

What is wkb?
 
  • #11
bgq said:
What is wkb?

It's a numerical approximation method discovered by Wentzel, Kramers, and Brillouin.
 
  • #13
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
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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