Quantum Mechanics Mock Tests

The Heisenberg uncertainty principle states that the product of the uncertainties in position and momentum is:

The commutator [x̂, p̂²] is equal to:

A particle of mass m is confined in a one-dimensional infinite potential well of width L (0 < x < L). The energy of the nth excited state is:

The normalization constant for the wavefunction ψ(x) = A e^(-αx²) (Gaussian) is:

If the uncertainty in the position of a particle is Δx, the minimum uncertainty in its momentum Δp satisfies (where ℏ = h/(2π)):

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:

In time-independent perturbation theory, the first-order correction to the energy eigenvalue E_n^(1) is: