Quantum Mechanics Mock Tests

The commutator [x, p²] is equal to:

The de Broglie wavelength of a particle with momentum p is:

The variational method in quantum mechanics provides an upper bound to the ground state energy. If ψ_trial is a normalized trial wavefunction, then:

The Dirac equation for a free relativistic particle of mass m is:

The expectation value of the kinetic energy for a particle in the ground state of a 1D infinite square well of width L is:

The quantum tunneling probability through a rectangular potential barrier of height V₀ and width a (for E < V₀) is approximately proportional to:

The Hamiltonian of a simple harmonic oscillator H = p²/(2m) + (1/2)mω²x² can be written in terms of creation (a†) and annihilation (a) operators as:

The energy levels of a particle in a one-dimensional infinite square well of width L are proportional to: