# Double Potential Well: Wave Function & Forces

• michael879
In summary: The conversation discusses a homework assignment where the wave function of a particle in a double potential well was found. It was observed that as the distance between the wells decreased, the energy of the system also decreased, suggesting an attractive force pulling the wells together. This idea was extended to explain gravity, with composite particles acting as potential wells and quarks having wave functions that extend to other wells. However, this may not fully explain gravity and the concept of wave function overlap was also discussed. The conversation also clarifies that electrons do not interact with themselves, but Coulomb interaction must be considered for multiple electrons.
michael879
I remember this homework assignment I did a while back, where we "found" the wave function of a particle in a double potential well. The distance between them was variable and we found that as the distance decreased, the energy of the system went down. This would suggest a force pulling the two wells together right? I know this doesn't explain repelling forces at all, but wouldn't this "work" as an explanation of a force like gravity? treat composite particles as potential wells, and quarks as particles with a wave function that extends to all the other wells (its incredibly small everywhere but the particle its in). Particles made of quarks would feel a weak attractive force to each other.

I doubt this actually works to explain gravity, and maybe the quark example is ridiculous since their wave function is pretty confined. However, anything that acts a well would have this attractive force wouldn't it?

No it's a question of overlap of wave functions in the barrier region, which becomes significant if the distance between the wells decreases (or the barrier is low).

$$\Psi(x)=c_1\Psi_1(x)+c_2\Psi_2(x)$$,

where Psi_1 and Psi_2 are local (approximative) solutions to the "uncoupled" problem, but with some decay into the barrier (like gaussian, for instance).

The penetration of the wave function into the finite barrier add an extra energy:

$$\Delta E =V_{barr}\int_0^L \Psi^2(x)\;dx$$,

where L is the thickness of the barrier.

The electron does not interact with itself! There is no such term in the Hamiltonian. If you have many electrons you would have to include Coulomb interaction of course.

/Per

I can understand the thought process behind this explanation and it is an interesting concept. However, it is important to note that the concept of a double potential well and the associated wave function and forces are based on quantum mechanics, which is a theory that describes the behavior of particles at a very small scale. On the other hand, gravity is a macroscopic force that operates at a much larger scale, and it is described by the theory of general relativity. Therefore, while it is intriguing to think about particles and quarks as potential wells and their wave functions potentially explaining gravity, it is not a scientifically accepted explanation.

Furthermore, the idea of treating composite particles as potential wells and quarks as particles with a wave function that extends to other wells may not accurately represent the complex interactions and dynamics of these particles. It is important to remember that scientific theories and explanations are constantly evolving and being refined, and it is crucial to base our understanding on evidence and experimental data.

In conclusion, while the concept of using potential wells and wave functions to explain forces such as gravity may seem appealing, it is not a scientifically supported explanation and more research and evidence is needed to fully understand and describe these phenomena.

## 1. What is a double potential well?

A double potential well is a concept in quantum mechanics that describes a system with two potential energy wells. This means that the system can exist in two distinct energy states, with a barrier separating the two wells.

## 2. How does the wave function behave in a double potential well?

The wave function in a double potential well will have two distinct peaks, corresponding to the two potential energy wells. It will also have a lower amplitude in the region between the wells, due to the barrier separating them.

## 3. What are the forces acting on a particle in a double potential well?

The forces acting on a particle in a double potential well are the potential energy forces. These forces will push the particle towards the bottom of each well, and away from the barrier between the wells.

## 4. How does the energy of a particle in a double potential well relate to its wave function?

The energy of a particle in a double potential well is directly related to its wave function. The higher the energy, the wider the wave function will be, and the more likely the particle is to be found in the region between the potential energy wells.

## 5. What is the significance of a double potential well in quantum mechanics?

A double potential well allows us to study the behavior of particles in a system with multiple energy states. It also helps us understand the effects of barriers on particle behavior, and has applications in various fields such as solid state physics and molecular dynamics.

• Quantum Physics
Replies
8
Views
1K
• Quantum Physics
Replies
10
Views
2K
Replies
19
Views
961
• Quantum Physics
Replies
5
Views
1K
• Quantum Physics
Replies
23
Views
2K
• Quantum Physics
Replies
14
Views
1K
• Quantum Physics
Replies
2
Views
1K
• Quantum Physics
Replies
15
Views
1K
• Quantum Physics
Replies
2
Views
1K
• Quantum Physics
Replies
6
Views
925