Question

Which of the equations below is the ground-state wavefunction for a particle?

a) Ψ = e^(-ikx)
b) Ψ = sin(kx)
c) Ψ = e^(-kx)
d) Ψ = cos(kx)

Answer 1

The ground-state wavefunction for a particle is the wavefunction that represents the lowest energy state of the particle. Out of the given options, the ground-state wavefunction can be represented by the equation Ψ = sin(kx) (option b).

Step-by-step explanation:

The ground-state wavefunction for a particle is the wavefunction that represents the lowest energy state of the particle. In quantum mechanics, the ground state is often denoted as the state with the lowest energy, or the state closest to the potential energy minimum.

Out of the given options, the ground-state wavefunction for a particle would be represented by the equation Ψ = sin(kx) (option b). This is because the ground state typically corresponds to a node in the wavefunction, which is represented by a sine function.

The other equations do not represent the ground state. For example, option a is an exponential function, options c and d are cosine functions, which do not have nodes and do not represent the lowest energy state.