## Probability of Finding a Particle

## Prove that the total probability of finding a particle is conserved.

The norm of a state vector is given by: .

In order to prove that the probability of finding a particle is *conserved*, we must obtain that

Now, we recall that from the 6th Postulate of Quantum Mechanics, the time evolution of the state vector is governed by the Schrodinger Equation as,

[1]

[2]

Taking the conjugate,

[3]

but since by definition is Hermitian, that is, , then

[4]

Now, taking the scalar product of equations [4] and [2],

[5]

Substituting equations [2] and [4],

[6]

[7]

[8]

[9]

Hence, the** total probability of finding a particle is conserved** , since we obtained that

.

#### By: Joshua J. Ordeniza, MS Physics Student, MSU-IIT