(Schrodinger's Equations - STIE and STDE

Schrodinger wave equation

State the Schrodinger equation for a particle moving in one dimensionand show how it is related to the motion of electrons in atoms

Which conditions correspond to STP?

Question 4What is the time-dependent Schrödinger equation for a particle in a potential 𝑉=12𝑚𝜔2𝑥2V= 21​ mω 2 x 2 ?1 point𝑖ℏ∂𝜓∂𝑡=12𝑚𝜔2𝑥2iℏ ∂t∂ψ​ = 21​ mω 2 x 2 𝑖ℏ∂𝜓∂𝑡=−ℏ2∇22𝑚𝜓+12𝑚𝜔2𝑥2𝜓iℏ ∂t∂ψ​ =− 2mℏ 2 ∇ 2 ​ ψ+ 21​ mω 2 x 2 ψ(𝑖ℏ∂∂𝑡+12𝑚𝜔2𝑥2)𝜓=𝐸𝜓(iℏ ∂t∂​ + 21​ mω 2 x 2 )ψ=Eψ𝑖ℏ∂𝜓∂𝑡=−ℏ2∇22𝑚𝜓+12𝑚𝜔2𝑥2iℏ ∂t∂ψ​ =− 2mℏ 2 ∇ 2 ​ ψ+ 21​ mω 2 x 2

Schrodinger wave equation for a particle in one-dimensionalbox. What is zero point energy of a particle in one-dimensional box? Why the energy of the particle cannot bezero at zero point energy