QM Applications: Particle-in-a-Box (Derivation)

The video tutorial explains the time-independent Schrodinger equation and its application to the particle in a box model. It covers the concept of potential energy within the box, the derivation of the wave function, and the energy expression for a particle in a one-dimensional box. The tutorial also discusses the implications of infinite and finite potential energy wells, emphasizing the importance of memorizing the energy expression for exams.

What is the potential energy of a particle inside a one-dimensional box?

• Depends on the position

• Equal to the kinetic energy

• Infinite

• Zero

Why can't a particle leave the one-dimensional box?

• The walls are too high to climb

• The potential energy outside the box is infinite

• The particle is too heavy

• The box is sealed

In the context of a particle in a box, what does quantization refer to?

• The particle's energy levels are discrete

• The particle can move freely

• The particle's position is fixed

• The particle's speed is constant

What assumption is made about the potential energy inside the box when solving the Schrodinger equation?

• It varies with time

• It is infinite

• It is zero

• It is constant

What is the form of the wave function used for a particle in a box?

• A times the cosine of NPI X over a

• A times the sine of NPI X over a

• A times the exponential of NPI X over a

• A times the tangent of NPI X over a

What is the significance of the wave function in the Schrodinger equation?

• It represents the particle's charge

• It represents the particle's mass

• It represents the particle's probability distribution

• It represents the particle's speed

What is the final expression for the energy of a particle in a one-dimensional box?

• H^2 n^2 / 8 MA

• H^2 n^2 / 16 MA

• H^2 n^2 / 4 MA

• H^2 n^2 / 2 MA

What happens to the energy expression when the potential energy is not zero inside the box?

• It remains the same

• It becomes undefined

• It changes to a different form

• It becomes zero

What is the term used for a potential energy well where the potential energy is infinite at the walls?

• Infinite potential energy well

• Finite potential energy well

• Zero potential energy well

• Variable potential energy well

How does the finite well model differ from the infinite well model?

• The potential energy varies with time

• The potential energy is zero inside the box

• The potential energy is finite at the walls

• The potential energy is infinite at the walls