Exploring Quantum Harmonic Oscillator

What is the ground state energy of a quantum harmonic oscillator?

• E_0 = (1/4)ħω

• E_0 = ħω

• E_0 = ħω/2

• E_0 = (1/2)ħω

Which equation describes the potential energy of a harmonic oscillator?

• U = mgh

• U = kx + c

• U = (1/2)mv^2

• U = (1/2)kx^2

What is the significance of the zero-point energy in quantum mechanics?

• Zero-point energy represents the lowest energy state of a quantum system, highlighting the inherent fluctuations in quantum mechanics.

• Zero-point energy has no relevance in quantum mechanics.

• Zero-point energy is only applicable in classical physics.

• Zero-point energy is the maximum energy state of a quantum system.

How does the quantum harmonic oscillator differ from a classical one?

• The quantum harmonic oscillator can have any energy value, similar to classical oscillators.

• The quantum harmonic oscillator has quantized energy levels, unlike the classical harmonic oscillator which has continuous energy.

• Classical harmonic oscillators can exist in superposition states, unlike quantum ones.

• The quantum harmonic oscillator has a fixed energy level like a classical one.

What are the allowed energy levels of a quantum harmonic oscillator?

• E_n = nħω, n = 0, 1, 2, ...

• E_n = (n^2)ħω, n = 0, 1, 2, ...

• E_n = (n + 1)ħω, n = 0, 1, 2, ...

• E_n = (n + 1/2)ħω, n = 0, 1, 2, ...