# QM - Wedge-shaped potential - Uncertainty Principle

• wombat4000
In summary, the conversation is about a question related to quantum mechanics and a wedge-shaped potential. The person is struggling to understand the concept and has been seeking help online and in textbooks. The potential consists of two conductor plates forming an angle and the person is trying to figure out how to approach the problem. They mention the potential being infinite for x < 0 and increasing linearly for x > 0. They also mention solving the time independent Schrodinger equation and finding wavefunctions to determine the standard deviations and variances of momentum and position.

## Homework Statement

See lower down for question

## The Attempt at a Solution

I have been trying to find help with this question on the net and in my textbooks. I am really struggling with QM, i don't know where to start - i appreciate what the graph of the wedge-shaped potential looks like but i just don't understand the rest of it.

Last edited by a moderator:
Does it mean that one has two conductor plates with the edges close or touching (but well insulated) and the planes form an angle (looking along the planes parallel to the closer for common edges?

Also, please be patient and don't bump with multiple posts.

That would make sense i guess.

(Sorry about the multiple posts - i couldn't post the URL without having 15 or more posts.)

still no joy though.

OK, now I get it. I was think an electostatic problem, which this isn't.

I presume one has an idea of what to do if one has a potential V(x).

Well the potential in infinite for x < 0. V(0) = 0, and V(x) = bx, x >0, so it inreases linearly with slope b, i.e. like a ramp function, as opposed to being constant, for example.

It's been 30+ years since I've done this type of calc, so bear with me, and I'll get others to look in.

much appreciated.

I think you need to solve the time independent schrodinger equation for this potential, find the stationary state wavefunctions, and then find the standard deviations and variances of the momentum and position

## 1. What is the wedge-shaped potential in quantum mechanics?

The wedge-shaped potential is a concept in quantum mechanics that refers to a potential energy surface that is shaped like a wedge. This type of potential energy surface is commonly used to model the behavior of particles in a confined space, such as a narrow channel or a thin film. It is a commonly used model in quantum mechanics due to its simplicity and ability to accurately predict particle behavior.

## 2. How does the wedge-shaped potential affect the behavior of particles?

The wedge-shaped potential affects the behavior of particles by confining them to a narrow region. This confinement leads to changes in the particle's energy levels and wave function, causing them to exhibit wave-like behavior and experience quantum tunneling. The shape of the potential also influences the probability of finding a particle in a specific location within the wedge.

## 3. What is the Uncertainty Principle in quantum mechanics?

The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to know the exact position and momentum of a particle simultaneously. This principle is a consequence of the wave-particle duality of quantum mechanics and places a fundamental limit on the precision of our measurements in the quantum world.

## 4. How does the Uncertainty Principle relate to the wedge-shaped potential?

The Uncertainty Principle is closely related to the wedge-shaped potential as it is a direct consequence of the confined nature of the potential. The uncertainty in a particle's position and momentum is directly affected by the shape and strength of the potential. In a wedge-shaped potential, the uncertainty in a particle's position increases as the potential becomes steeper, making it more difficult to determine the particle's location.

## 5. Can the Uncertainty Principle be violated in the wedge-shaped potential?

No, the Uncertainty Principle cannot be violated in the wedge-shaped potential or any other scenario in quantum mechanics. It is a fundamental principle of the quantum world and has been confirmed through numerous experiments. However, in certain cases, the uncertainty in one of the particle's properties can be reduced at the expense of increasing the uncertainty in the other property, but the overall uncertainty cannot be completely eliminated.