Understanding Quantum Mechanics in a Particle Box

What is the nature of the potential inside the one-dimensional box where the particle is trapped?

• Negative potential inside the box

• Variable potential inside the box

• Zero potential inside the box

• Infinite potential throughout the box

How is the De Broglie wavelength of a particle related to its momentum?

• It is unrelated to the momentum

• It is directly proportional to the momentum

• It is inversely proportional to the momentum

• It is equal to the momentum

What is the expression for the momentum of a particle in terms of Planck's constant and the box length?

• p = h / l

• p = 2h / l

• p = h / 2l

• p = 2l / h

What is the formula for the minimum energy of a particle in a box?

• E = h^2 / 4l^2m

• E = h^2 / 8l^2m

• E = h^2 / 2l^2m

• E = h^2 / 16l^2m

Why can't a particle in a box have zero energy according to quantum mechanics?

• Because of the zero-point energy

• Due to the presence of external forces

• Because of the infinite potential barriers

• Due to the particle's mass