Lowest Energy of Particle in 1-D Box: 2 eV

• Amith2006
In summary, the conversation discusses a particle inside a one dimensional box with impenetratable walls and an energy eigenvalue of 2 eV. The individual attempts to solve the problem by using the equation E(n) = (n^2)E(o), but realizes that more information is needed such as the mass and length of the box or the quantum number describing the 2eV eigenstate. However, after seeing a diagram, they are able to determine that the quantum number is n=2 and the zero point energy is E(o) = 0.5 eV.

Homework Statement

1) A particle inside a one dimensional box with impenetratable walls at x=-a and x=+a has an energy eigenvalue of 2 eV. What is the lowest energy that the particle can have?

Homework Equations

E(n) = (n^2)E(o)
where E(o)=h^2/(8mL^2)

The Attempt at a Solution

I started in the following way:
If E(o) is the zero point energy. Then,
2 eV = (n^2)E(o)

I don't think it leads anywhere else. Are you sure they didn't give you some other kind of information?

I forgot to include the wave function of the particle. When u asked whether any other information was given, I struck a way to solve this problem.
I solved it in the following way:
Let w denote the wave function of the particle.
w(n)= [n^2]E(o)
From the wave function of the particle it is clear that n=2
w(2)=2 eV = [2^2]E(o)
i.e. E(o) = 0.5 eV
Is it right?

Attachments

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The problem is still ill-determined pending knowledge of either the mass and length of the box, or the quantum number (n) describing the 2eV eigenstate. Perhaps you are given a picture of the wavefunction for the 2eV eigenstate? If so, you can count zeros to determine the quantum number, otherwise, there isn't enough information to answer the problem.

The problem is still ill-determined pending knowledge of either the mass and length of the box, or the quantum number (n) describing the 2eV eigenstate. Perhaps you are given a picture of the wavefunction for the 2eV eigenstate? If so, you can count zeros to determine the quantum number, otherwise, there isn't enough information to answer the problem.

Did u see the diagram? Isn't that enough to solve the problem?

Amith2006 said:
I forgot to include the wave function of the particle. When u asked whether any other information was given, I struck a way to solve this problem.
I solved it in the following way:
Let w denote the wave function of the particle.
w(n)= [n^2]E(o)
From the wave function of the particle it is clear that n=2
w(2)=2 eV = [2^2]E(o)
i.e. E(o) = 0.5 eV
Is it right?

That's right.

Thats cool!I think I am getting better. Thanks.

1. What is the significance of the "Lowest Energy of Particle in 1-D Box: 2 eV"?

The "Lowest Energy of Particle in 1-D Box: 2 eV" is a theoretical concept used in quantum mechanics to describe the energy level of a particle confined to a one-dimensional box. It represents the minimum energy that a particle can possess within the box and has important implications for understanding the behavior of particles in quantum systems.

2. How is the lowest energy of a particle in a 1-D box calculated?

The lowest energy of a particle in a 1-D box is calculated using the Schrödinger equation, which is a fundamental equation in quantum mechanics that describes the behavior of particles in a given system. This equation takes into account the size and shape of the box, as well as the mass and energy of the particle, to determine the lowest possible energy that the particle can have within the box.

3. Can the lowest energy of a particle in a 1-D box ever be less than 2 eV?

No, the lowest energy of a particle in a 1-D box can never be less than 2 eV. This is because the energy levels in quantum systems are quantized, meaning they can only take on certain discrete values. The lowest energy level is always 2 eV, and any lower energy state would violate the laws of quantum mechanics.

4. How does the size of the 1-D box affect the lowest energy of the particle?

The size of the 1-D box has a direct impact on the lowest energy of the particle. As the size of the box decreases, the lowest energy level also decreases. This is because a smaller box creates a stronger confinement for the particle, causing it to have a lower energy state.

5. What real-world applications does the concept of the lowest energy of a particle in a 1-D box have?

The concept of the lowest energy of a particle in a 1-D box has many real-world applications, particularly in the field of nanotechnology. Understanding the energy levels of particles in confined spaces is crucial for designing and manipulating nanoscale devices and materials. It also has implications for understanding the behavior of electrons in electronic devices, such as transistors and semiconductors.