Solving Problems Using Quantum Mechanics

In summary: Thank you for your question. Newton's 2nd Law holds in the quantum world as long as the system is not in a superposition of states. However, it is not possible to find the system in a superposition of states, so using Newton's 2nd Law is not possible.
  • #1
bgq
162
0
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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  • #2
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
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
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.
 
  • #5
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
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?
 
  • #7
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
yes,you can find the energy by using wkb approximation,if particle is confined to above Z=0 by a perfectly reflecting plane?
 
  • #9
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?
 

1. What is quantum mechanics?

Quantum mechanics is a branch of physics that explains the behavior of particles at the atomic and subatomic level. It involves mathematical equations and principles to understand the nature of particles and their interactions.

2. How can quantum mechanics be used to solve problems?

Quantum mechanics can be used to solve problems by providing a framework to calculate the behavior of particles and systems at the quantum level. It can also be used to develop new technologies such as quantum computers and sensors.

3. What are some real-world applications of quantum mechanics?

Some real-world applications of quantum mechanics include transistors in electronic devices, magnetic resonance imaging (MRI) machines, and cryptography for secure communication.

4. Is quantum mechanics difficult to understand?

Quantum mechanics can be complex and difficult to understand due to its abstract concepts and mathematical nature. However, with proper study and application, its principles can be comprehended and utilized.

5. What are some challenges in using quantum mechanics to solve problems?

Some challenges in using quantum mechanics to solve problems include the need for advanced mathematical skills, the complexity of quantum systems, and the difficulty in controlling and measuring particles at the quantum level.

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