# Particles in a Box Homework: A,B,C,D

• lotrsimp12345
In summary, the conversation discusses a one-dimensional box and a two-dimensional square box with particles of mass m and energies of 13*pie^2h^2/2mL^2 and 10pie^2h^2/2mL^2, respectively. The discussion also touches on the concepts of states, degeneracy, and the maximum number of particles that can occupy each state.
lotrsimp12345

## Homework Statement

(a)Think of a one-dimensional box of length L. There are two identical, non classical particles of mass m in the box. The total energy of the system is 13*pie^2h^2/2mL^2. What states are occupied by by the two particles?
(B) If a single non-classical particle of mass m in a two dimensional square box of side length L has energy 10pie^2h^2/2mL^2 what state is it in?
(C) Are the states found in A and B degenerate or nondegenerate?
(d) What is the maximum number of particles that can be in each state?

## The Attempt at a Solution

(a) I was able to find the energy levels to be n1=2 and n2=3 but what do they mean by states? Are you not supposed to have orbital quantum number and ml and ms? and why is that?

(b) since it is a two dimensional box it has two directions nyf= 3 or 1 and nxf=1 or 3. The energies should add since it is a 2 dimensional box correct?
(c) i have no idea what degenerate means. My teacher tells us that both a and b are degenerate. Is this because they have different energy levels? he said it has something to do with wave function.
(d) no idea think its either boson or fermion but not sure how to know without knowing wave function.

(a) I was able to find the energy levels to be n1=2 and n2=3 but what do they mean by states? Are you not supposed to have orbital quantum number and ml and ms? and why is that?
You can also have n1=3 and n2=2. And states are defined by the quantum numbers, so |2,3> is a state as well as |3,2>. You don't have orbital quantum numbers because this is a 1D problem.

(c) i have no idea what degenerate means. My teacher tells us that both a and b are degenerate. Is this because they have different energy levels? he said it has something to do with wave function.
Degenerate just means that more than one state has the same energy. And both (a) and (b) have two possible states for the given energies.

(d) no idea think its either boson or fermion but not sure how to know without knowing wave function.
Does it specify somewhere that they are bosons or fermions?

when i asked him he said their are two kinds of particles. the normal one's we think of and then their are these other ones. So i am assuming they are bosons and fermions.

anyone know how to do part d?

## 1. What is the concept of "Particles in a Box"?

The concept of "Particles in a Box" is a theoretical model used in quantum mechanics to study the behavior of particles confined within a finite and enclosed space. The box represents the boundaries of the system and the particles are considered to have no interactions with the external world.

## 2. What is the purpose of the A,B,C,D homework in "Particles in a Box"?

The A,B,C,D homework in "Particles in a Box" is designed to help students understand and apply the principles and equations of quantum mechanics to solve problems related to particles confined in a box. It also helps them develop critical thinking and problem-solving skills.

## 3. How does the size of the box affect the behavior of the particles?

The size of the box has a direct impact on the behavior of the particles. A smaller box will result in higher energy levels for the particles, while a larger box will have lower energy levels. Additionally, the size of the box also affects the probability of finding the particles in certain locations within the box.

## 4. What are the boundary conditions in "Particles in a Box"?

The boundary conditions in "Particles in a Box" refer to the restrictions placed on the wave function of the particles at the boundaries of the box. The most commonly used boundary conditions are periodic boundary conditions, where the wave function must be continuous at the boundaries, and fixed boundary conditions, where the wave function must be zero at the boundaries.

## 5. How is "Particles in a Box" related to real-world applications?

"Particles in a Box" may seem like a theoretical concept, but it has real-world applications in many areas, such as semiconductor physics, where the behavior of electrons in a confined space is crucial for understanding the properties of materials used in electronic devices. It is also used in the study of atoms and molecules, as well as in the development of new technologies like quantum computing.

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