Question

The time derivative of probability of finding a particle

Answer 1

We want to solve the time independent Schrödinger equation
{\displaystyle {\hat {H}}(x)\psi (x)=E\psi (x)}
{\displaystyle \left\lbrace -{\frac {\hbar ^{2}}{2m}}{\frac {\partial ^{2}}{\partial x^{2}}}+V(x)\right\rbrace \psi (x)=E\psi (x)} (Eq. 1)
for some specific case. We will consider a few different potential energies V(x) and see what the eigenvalues and eigenfunctions look like. We will also practice with some numerical exercises while making several observations on the behaviour of quantum particles. From now on, we may refer to the time independent Schrödinger equation as just the 'Schrödinger' equation.