The compact form of Schrodinger wave equation is

Question

Question

Answer 1

Concept:

Schroedinger wave equation:

Schrodinger wave equation is a mathematical expression describing the energy, momentum, and position of the electron in space and time.
The Schrödinger equation (also known as Schrödinger’s wave equation) is a partial differential equation that describes the dynamics of quantum mechanical systems via the wave function.

Explanation:

The one-dimensional time-dependent Schrödinger equation for a free particle is

\( i\hbar\frac{d \psi }{dt}=[-\frac{\hbar^{2}}{2m}\nabla^{2}+V(x)]\Psi\)

Where Ψ(x,t) = Wave function

h = Planck constant

m = mass

As we know, mathematically Hamilton operator can be written as

\(H =[-\frac{\hbar^{2}}{2m}\nabla^{2}+V(x)]\)

And Energy operator is

\(E = i\hbar\frac{d}{d t}\)

Therefore, the compact form of the Schroedinger wave equation is

\( i\hbar\frac{d \psi }{dt}=H\psi \)