Ground and Excited States in a Potential Well (QM)

In summary, the problem is to determine the energy levels for the first state of a particle in a potential well, starting at E0 and ending at 5a. The following states are sine waves at higher frequencies. The question is whether to draw a high-frequency sine wave with a decrease in amplitude at the jump at 2a, or to keep the amplitude constant and decrease the frequency at the jump. The book only mentions an infinite square well and does not provide further explanation. It is unclear if the energy level of 0 is relevant, as a particle cannot have an energy level below the ground state (E0). The significance of the potential jump in the middle is also unclear.
  • #1
Poop-Loops
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Here's the problem:

http://www.phys.washington.edu/users/karch/324/2007/hw3.pdf

Just the first one.

Okay, so my understanding is that the first state of Psi (ground state) is just an arc, like a Gaussian distribution, starting from 0 at E0 and finishing at 5a also at the level of E0.

The next ones are just sine waves at higher frequencies.

So would I just draw a high frequency sine wave of amplitude E0 until I get to the "jump" at 2a, and then just decrease the the amplitude that that point, but keep the frequency the same?

Or since the frequency corresponds to energy, and I don't have as much of a jump from E0 to the bottom of the well, I should keep the amplitude constant the whole time, but decrease the frequency once I get to the "jump" at 2a?

The book only mentions an infinite square well and doesn't really go into it.
 
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  • #2
Sorry, but I still haven't figured this one out.

Is the energy level 0 meaningless here, since a particle can't get below the ground state (E0) in energy?

So it would be a high-frequency sine wave with the amplitude being from E to E0? I still don't see the significance of the potential jump in the middle.
 

1. What is a potential well in quantum mechanics?

A potential well in quantum mechanics is a region of space where the potential energy of a particle is lower than the surrounding areas. This creates a “well” where the particle is more likely to be found and is typically represented as a curved, concave shape in a graph of potential energy versus position.

2. What are ground and excited states in a potential well?

The ground state in a potential well is the lowest energy state that a particle can occupy. This is where the particle is most stable and has the highest probability of being found. Excited states, on the other hand, are higher energy states that a particle can occupy by absorbing energy from its surroundings. These states are less stable and have a lower probability of being occupied.

3. How do particles behave in a potential well?

Particles in a potential well behave according to the principles of quantum mechanics. This means that they can exist in multiple states simultaneously and their exact position and energy cannot be known with certainty. The probability of finding a particle in a certain state is determined by its wave function, which is described by the Schrödinger equation.

4. What is the significance of ground and excited states in a potential well?

The ground and excited states in a potential well have important implications for the behavior of particles and their interactions with each other. For example, the energy difference between these states can determine the absorption or emission of photons by atoms, leading to the creation of light and other electromagnetic radiation.

5. How are ground and excited states in a potential well experimentally observed?

The energy levels of particles in a potential well can be experimentally observed through various techniques such as spectroscopy, where the absorption or emission of light is measured. Other methods include using lasers to excite particles to higher energy levels and observing their subsequent decay to the ground state. These experiments provide valuable insights into the behavior and properties of particles in a potential well.

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