Question

Which of the following is the correct expression for the Schrödinger wave function?

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

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

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

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

This question was posed to me in an international level competition.

The query is from Schrodinger Equation (Time Dependent Form) topic in division Quantum Physics of Engineering Physics I

Answer 1

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

The explanation: The correct expression for the Schrödinger wave equation is \(i\hbar \frac{d\Psi}{dt}= -i\frac{\hbar^z}{2m} \frac{\partial^2\Psi}{\partial x^2}+ U\Psi \). Schrodinger equation is a basic principle in itself.