# Infinity potential hole - transition to base state

• lakmus
In summary, the conversation discusses the probability of a particle transitioning from the first excited state to the base state in an infinity potential hole. The speaker notes that the probability appears to be zero due to the orthogonality of the eigenfunctions, but there is no error and the energy eigenstates are stable. They also refer to a thread discussing a similar topic for a H-atom.
lakmus
Hi!
I try to figure out the probability (sure as function of parameter time) of
transition particle in the hole from the first excitation state to the base
state in an infinity potential hole. Because the eigenfuncion of particle there
are orthogonal, the probability looks like zero - where could be the problem?

Thanks!

There is no error at all - energy eigenstates are stable.
In reality, some external disturbance would suffice to get the electron to fall to the ground state. We discussed this briefly (for a H-atom) in this thread:
(on the second page)

## 1. What is an infinity potential hole?

An infinity potential hole is a theoretical concept in quantum mechanics where the potential energy is infinite at a certain point in space. This creates a "hole" in the potential energy well, where particles cannot exist.

## 2. How does a particle transition to the base state in an infinity potential hole?

In an infinity potential hole, particles cannot exist at the point of infinite potential. Therefore, when a particle is in this region, it will experience a force that pushes it towards the base state, which is the lowest energy state of the system.

## 3. What is the significance of the base state in an infinity potential hole?

The base state represents the lowest energy state of the system. In an infinity potential hole, particles will naturally be drawn to this state, as it is the most stable and energetically favorable state for them to exist in.

## 4. Can particles exist in the region of the infinity potential hole?

No, particles cannot exist at the point of infinite potential in an infinity potential hole. However, they may exist in the regions surrounding the hole, where the potential energy is not infinite. These particles will experience a force that pushes them towards the base state.

## 5. How does an infinity potential hole relate to the uncertainty principle?

The uncertainty principle states that the position and momentum of a particle cannot be known simultaneously with absolute certainty. In an infinity potential hole, the uncertainty in the position of a particle becomes infinite, as it cannot exist at the point of infinite potential. This is one of the key concepts of quantum mechanics.

Replies
6
Views
1K
Replies
7
Views
1K
Replies
4
Views
730
Replies
3
Views
1K
Replies
11
Views
2K
Replies
6
Views
1K
Replies
1
Views
1K
Replies
2
Views
1K
Replies
15
Views
2K
Replies
5
Views
1K