Required math: calculus
Required physics: Schrödinger equation
Reference: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 2.4.
The stationary states of the infinite square well are given by
For we have
For the momentum we have
The uncertainty principle here is then:
The smallest uncertainty will be for the state and is approximately , which satisfies the condition .