Knowledge and understanding of QM

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Discussion Overview

The discussion revolves around the understanding of quantum mechanics, specifically focusing on the behavior of particles in finite potential wells, the concept of bound states, and the measurement of energy in different regions of potential. Participants explore theoretical implications, experimental observations, and the nuances of quantum measurements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to determine if a particle is in a region where the potential energy is greater than its energy in a finite potential well.
  • Another participant states that it is experimentally observed that particles can exist in "forbidden" regions with some probability, and quantum mechanics can be used to calculate this probability.
  • There is a discussion about the distinction between good position and good energy measurements, which can yield different results.
  • A participant expresses confusion about how to measure the energy of particles in different regions and seeks clarification on the measurement process.
  • Concerns are raised about the influence of temperature and noise on measurements in real experiments.
  • Participants discuss bound states in finite potential wells, noting that bound states exist when the energy is less than the potential, but question the conditions under which these states occur.
  • There is a debate about the existence of bound states in various configurations of potential wells, with some participants asserting that not all configurations guarantee bound states.
  • Clarifications are sought regarding the definitions of potential energies and the conditions necessary for bound states to exist.

Areas of Agreement / Disagreement

Participants express differing views on the measurement of energy and the conditions for bound states in potential wells. There is no consensus on how to approach these measurements or the implications of different potential configurations.

Contextual Notes

Participants highlight the complexity of measuring quantum states and the influence of external factors such as temperature and noise. The discussion also reflects the dependency on specific definitions and assumptions regarding potential wells and bound states.

Who May Find This Useful

This discussion may be of interest to students and researchers in quantum mechanics, particularly those exploring the concepts of potential wells, bound states, and measurement techniques in quantum systems.

LagrangeEuler
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In problem of infinite potential well particle can't be in a region where ##V=\infty##. How we know that in case of finite potential well that particle is in the region where ##V>E##. How we know what is energy of the particle in moment when we localize it in the region with potential ##V##. This is very hard for me to understand. Can u help me?
 
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LagrangeEuler said:
How we know that in case of finite potential well that particle is in the region where ##V>E##.
It is an experimental result that you can find the particles in those "forbidden" regions with some probability.
You can use quantum mechanics to calculate that probability.

How we know what is energy of the particle in moment when we localize it in the region with potential ##V##.
Do you want a good position or a good energy measurement? Those will lead to different results.
 
mfb said:
It is an experimental result that you can find the particles in those "forbidden" regions with some probability.
You can use quantum mechanics to calculate that probability.

Do you want a good position or a good energy measurement? Those will lead to different results.


That is not my question. I asked how we know energy of the particles in different region?
http://en.wikipedia.org/wiki/Finite_potential_well
"There are two possible families of solutions, depending on whether E is less than (the particle is bound in the potential) or E is greater than (the particle is free)."

How we know from measurement is it particle free or not?

I want to know more about this measurements. I know how to solve this problem with use og mathematics.
 
LagrangeEuler said:
That is not my question. I asked how we know energy of the particles in different region?
That does not exist. The particle has a unique [expectation value of the] energy, which does not depend on the position.

http://en.wikipedia.org/wiki/Finite_potential_well
"There are two possible families of solutions, depending on whether E is less than (the particle is bound in the potential) or E is greater than (the particle is free)."

How we know from measurement is it particle free or not?
Measure the energy of the particle ;). Or just see if it stays in the well (and in its direct vicinity) - if it does, it is not free, otherwise it is free.
 
I have a problem with this measurements. How they measure those quantities. In real experiment you will need to think about temperature, all other kinds of noise...

What about bond states in the well. If finite potential well is symmetric then for ##E<V##, there are bond states. If isn't symmetric then could be bound states. Why is that physically?
 
Temperature is a property of many particles at the same time, a single particle does not have a (meaningful) temperature.

What about bound states? Well, those are the states with E<V, what exactly are you asking?
And which symmetry do you mean?
 
If I have finite potential well with ##0>E>V_1<V_2## I don't have bond states for every ##V_1## and ##V_2##. Why I don't have it always.
 
What are V1, V2 (or where are they), and why do you have an E in the description of your potential?
Why I don't have it always.
In more than 1 dimension, some potential wells are so shallow that they do not have bound states. In 1 dimension, you always have a bound state.
 
It is one dimension square well. ##V_1## is potential for ##x<0##, ##V_2## is potential for ##x>a## and for ##0<x<a## potential is ##0##. Symbol for ##E## in the question isn't potential, it defines bond energy states. Can you please give me some answer?

No you don't have always bond state! That is the problem!
 
  • #10
That is not a potential well, that is a function with two steps (where the direction of the right step depends on the sign of V2). You need some global minimum in a limited range for a (proper) potential well.
 

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