Question

Write schrodinger’s time dependentand time independent wave equations of matter waves in one dimensional and state physical significance of these Equations. 

Answer 1

 1.ONE DIMENSIONAL TIME DEPENDENT SCHRODINGER EQUATION.
`(-ħ)/(2m ) × (Ə^2 Ψ(x,t) )/(Əx^2) + VΨ (x,t)  = jħ(ƏΨ(x,t))/(Ət)`

The first and second term on the left hand side represents the kinetic and potential energies respectively of the particles and the right hand side represents the total potential.

2.ONE DIMENSIONAL TIME INDEPENDENT SCHRODING EREQUATION.
`(ħ^2)/(2m) xx (d^2Ψ (x))/(dx^2) +V(x) Ψ (x) =EΨ(x)`

3.THREE DIMENSIONAL TIME INDEPENDENT SCHRODINGER EQUATION
`H = (ħ^2)/(2m)∇^2 + v`

Schrodinger equation is the fundamental equation of quantum mechanics. This is extremely
useful for investing various quantum mechanical problems.The wave function,the probability density,the energy values of a quantum  mechanical particle, etc. in various situation can be calculated with the help of this equation.