1000 Solved Problems in Modern Physics

Chapter 3

Quantum Mechanics – II

3.1 Basic Concepts and Formulae ................................

Schrodinger’s equation

i

∂ψ

∂t

=−

^2

2 μ

∇^2 ψ+V(r)ψ (3.1)

−

^2

2 μ

∇^2 ψ+(V−E)ψ=0 (Time independent equation) (3.2)

Probability densityρ=ψ∗ψ (3.3)

Continuity equation

∂ρ

∂t

+∇.j= 0 (3.4)

wherejis the probability current density.

Normalizationof the wave function

∫

all space

ρdτ=

∫

all space

ψn∗ψndτ= 1 (3.5)

I=

∫

ψmψndτis called the overlapping integral.

Orthogonality

∫+∞

−∞

ψn∗(x)ψm(x)dx= 0 ,ifm =n (3.6)

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