Question

Write the expression for the time independent schrodinger equation?​

Answer 1

• The total energy (E) of the particle can be written as T.E. = E = K.E. + P.E. is a Laplacian operator. Thus, the Time Dependent Schrödinger Equation, TDSE, can be derived from the wave mechanics considering the equations for a particle describing S.H.M

I hope it's helpful..!!

Answer 2

Answer:

Explanation:

Definition of  Schrodinger equation:

The wave function of a quantum mechanical system is controlled by the Schrödinger equation, which is a linear partial differential equation. It is an important outcome in quantum mechanics, and its discovery represented a turning point in the field's evolution.

Expression for the time independent Schrodinger equation:

As H=E, the time-independent Schrodinger  wave equation can be written.

$Hψ =Eψ$

H is referred to as a Hamiltonian operator.

The wave function is$Ψ$.

E is the system's energy.

$tˆ(H) = [-(h^ 2/8π^2m)(∂^2/∂x^ 2) +∂ ^ 2/(∂y^ 2+∂^ 2/∂z^2) +v]$

Since  $Ψ$is a function of the particle's positIon coordinates and is represented as  $Ψ (x.y.z),$

Equation (1) is spelled out as,

$[−(4^ 2/8π^ 2m)(∂^ 2ΨVx^ 2)+(∂^ 2Ψ∂y^ 2)+(V^2 Ψ∂z^ 2)+VΨ] =EPsi............$

Multiply the equation (3) by$−8π^2m/h^ 2$and rearranging $∂^2Ψ/∂x^ 2+∂x^2Ψ/∂y^ 2+∂^2Ψ/∂z^ 2+8π^ 2m/h2(E−V)Ψ=0$

It is known as a time independent Schrodinger wave equation because the Schrodinger wave equation in the previous equation  does not include time as a variable.

#SPJ3