Introduction to Quantum Mechanics · Problem 2.2

Time-Independent Schrödinger Equation — David J. Griffiths

Physics — Quantum Mechanics · energy_minimum

Problem

Show that EE must exceed the minimum value of V(x)V(x), for every normalizable solution to the time-independent Schrödinger equation. What is the classical analog to this statement? Hint: Rewrite Equation 2.5 in the form d2ψdx2=2mℏ2[V(x)−E]ψ;\frac{d^2\psi}{dx^2} = \frac{2m}{\hbar^2} [V(x) - E] \psi; if E<Vmin⁡E < V_{\min}, then ψ\psi and its second derivative always have the same sign—argue that such a function cannot be normalized.

Related theory

Browse the problem library