Particle in 1D Infinite Potential Box Problem in Quantum Mechanics

What is the general form of the wave function for a particle in a 1D infinite potential box?

• Ψ(x) = Aexp(kx) + Bexp(-kx)

• Ψ(x) = Asin(kx) + Bcos(kx)

• Ψ(x) = A/k sin(kx) + B/k sin(kx)

• Ψ(x) = A/k sin(kx) + B/k cos(kx)

What are the possible energy levels for a particle in a 1D infinite potential box?

• Negative energy levels

• Quantized energy levels given by En = n^2 * (h^2 / 8mL^2)

• Continuous energy levels

• Non-quantized energy levels

What is the expression for the eigenfunctions of a particle in a 1D infinite potential box?

• Exponential and logarithmic functions

• Sine and cosine functions

• Trigonometric functions

• Polynomial functions

How does the probability density of a particle in a 1D infinite potential box vary with position?

• Increasing within the box and zero outside the box

• Zero within the box and constant outside the box

• Constant within the box and zero outside the box

• Decreasing within the box and zero outside the box

What is the relationship between the energy levels and the wavelength of the particle in a 1D infinite potential box?

• Energy levels are inversely proportional to the square of the wavelength

• Energy levels are inversely proportional to the wavelength

• Energy levels are not related to the wavelength

• Energy levels are directly proportional to the square of the wavelength

What is the significance of the boundary conditions in the wave function of a particle in a 1D infinite potential box?

• Determining the allowed energy levels and the shape of the wave function within the box.

• Affecting the particle's mass

• Determining the color of the particle

• Creating a magnetic field within the box

How does the number of nodes in the wave function relate to the energy level of a particle in a 1D infinite potential box?

• The number of nodes in the wave function increases with the energy level of the particle.

• The number of nodes in the wave function is not related to the energy level of the particle.

• The number of nodes in the wave function is inversely proportional to the energy level of the particle.

• The number of nodes in the wave function decreases with the energy level of the particle.

What is the normalization condition for the wave function of a particle in a 1D infinite potential box?

• ∫|Ψ(x)|^2 dx = 1

• ∫Ψ(x) dx = 1

• ∫|Ψ(x)|^2 dx = 0

• ∫|Ψ(x)| dx = 1

How does the probability of finding the particle change in the 1D infinite potential box as the energy level increases?

• The probability of finding the particle increases

• The probability of finding the particle becomes negative

• The probability of finding the particle remains constant

• The probability of finding the particle decreases

What is the physical interpretation of the wave function for a particle in a 1D infinite potential box?

• Probability amplitude of finding the particle at a particular position within the box

• Color of the particle within the box

• Temperature of the particle within the box

• Speed of the particle within the box