Find spectrum given a potential. I have the solution, just need explanation.

In summary, the purpose of finding the spectrum given a potential is to understand the energy levels and possible states of a system, which is crucial in many areas of physics and chemistry. This is determined by solving the Schrödinger equation for the system and is influenced by factors such as the shape and depth of the potential, mass and charge of particles, and external interactions. The spectrum can change over time and is used to understand the properties of a system, such as binding energy and emission/absorption spectra, as well as its symmetry and other characteristics.
  • #1
lalover
19
0

Homework Statement


My teacher posted this solution. It is exactly what I had, except I did not have 4Pi in the numerator. Rather, I had 2 instead of 4, and I didn't have Pi. The solution manual has had mistakes before, so I am wondering if that's what the case is here. Every other step, I had identical. Can anyone please verify this? The question is the first attachment, and the solution is the other.


Homework Equations





The Attempt at a Solution

 

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  • #2
Ohh never mind I was misreading something. Sorry, no help is needed. Thanks.
 

Related to Find spectrum given a potential. I have the solution, just need explanation.

1. What is the purpose of finding the spectrum given a potential?

The purpose of finding the spectrum given a potential is to understand the energy levels and possible states of a system. This information is crucial in many areas of physics and chemistry, such as understanding the behavior of particles in a potential well or studying the electronic energy levels of atoms and molecules.

2. How is the spectrum determined from a given potential?

There are various mathematical methods used to determine the spectrum from a given potential. One common approach is to solve the Schrödinger equation for the system, which involves finding the eigenvalues and eigenvectors of the Hamiltonian operator. The energy levels of the system correspond to the eigenvalues, while the eigenvectors represent the quantum states.

3. What factors influence the spectrum of a system?

The spectrum of a system is influenced by several factors, including the shape and depth of the potential, the mass and charge of the particles in the system, and any external perturbations or interactions. These factors can affect the energy levels and states of the system, resulting in a unique spectrum for each system.

4. Can the spectrum of a system change over time?

Yes, the spectrum of a system can change over time due to various factors such as changes in the potential, interactions with other systems, or external perturbations. This is particularly relevant for systems that exhibit dynamical behavior, such as atoms in a changing electric field or particles in a time-dependent potential.

5. How can the spectrum be used to understand the properties of a system?

The spectrum provides valuable information about the energy levels and states of a system, which can be used to understand its properties. For example, the energy levels can be used to calculate the binding energy of particles in a potential well, or the emission and absorption spectra of atoms and molecules. Additionally, the states of a system can reveal its symmetry and other important characteristics.

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