Exploring Quantum Physics - Week 1 Question 9

Question:

Suppose that $\psi_1$ and $\psi_2$ satisfy the time independent Schrödinger equation for some potential. Which of the following necessarily also satisfies the Schrödinger equation?

Solution:

The correct choice is $c_1 \psi_1 + c_2 \psi_2$. This is because the Schrödinger equation is linear and homogeneous.