FREE IGNOU BCHCT 131 SOLVED ASSIGNMENT 2023




Question 3: Derive the time independent Schrödinger equation for a particle.

The time-independent Schrödinger equation for a particle is derived from the Schrödinger equation by separating the time-dependent and time-independent parts. The Schrödinger equation is given by:

-ħ²/2m * ∇²Ψ + VΨ = iħ∂Ψ/∂t

By assuming that the wave function Ψ can be written as a product of a spatial part and a time-dependent part (Ψ(x, t) = ψ(x) * φ(t)), and then separating variables, you can derive the time-independent Schrödinger equation:

-ħ²/2m * d²ψ/dx² + V(x)ψ = Eψ

Here, ψ(x) is the spatial wave function, V(x) is the potential energy, E is the total energy of the particle, and ħ is the reduced Planck constant.