Double Potential Well: Wave Function & Forces

[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?

 

[per.sundqvist]

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).

[tex]\Psi(x)=c_1\Psi_1(x)+c_2\Psi_2(x)[/tex],

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:

[tex]\Delta E =V_{barr}\int_0^L \Psi^2(x)\;dx[/tex],

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

 

[denian]

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.