Introduction to Quantum Mechanics · Problem 2.17

Time-Independent Schrödinger Equation — David J. Griffiths

Physics — Quantum Mechanics · free_particle_wave_functions

Problem

Show that [Aeikx+Be−ikx]\left[Ae^{ikx} + Be^{-ikx}\right] and [Ccos⁡kx+Dsin⁡kx][C\cos kx + D\sin kx] are equivalent ways of writing the same function of xx, and determine the constants CC and DD in terms of AA and BB, and vice versa. *Comment:* In quantum mechanics, when V=0V = 0, the exponentials represent *traveling* waves, and are most convenient in discussing the free particle, whereas sines and cosines correspond to *standing* waves, which arise naturally in the case of the infinite square well.

Related theory

Browse the problem library