Question

Which of the following is the correct expression for the steady-state form of Schrödinger wave function?

(a) \(P\Psi= -i\frac{\hbar}{2m}\frac{\partial\Psi}{\partial x}+U\Psi\)

(b) \(E\Psi= -i\frac{\hbar}{2m}\frac{\partial^2\Psi}{\partial x^2}+U\Psi\)

(c) \(E\Psi = -i\frac{\hbar^z}{2m}\frac{\partial\Psi/\partial x}+U\Psi\)

(d) \(E\Psi = -i\frac{\hbar^z}{2m}\frac{\partial^2\Psi}{\partial x^2}+U\Psi\)

I got this question in class test.

I would like to ask this question from Schrodinger Equation (Steady State Form) topic in portion Quantum Physics of Engineering Physics I

Answer 1

Right option is (d) \(E\Psi = -i\frac{\hbar^z}{2m}\frac{\partial^2\Psi}{\partial x^2}+U\Psi\)

To explain: The correct expression for the Steady state form of the Schrödinger wave equation is \(E\Psi = -i\frac{\hbar^z}{2m}\frac{\partial^2\Psi}{\partial x^2}+U\Psi\). It is different from the time-dependent for, as it depends on position of the particle only.