Consider a particle of mass m confined in a one-dimensional box of length L. In addition, suppose the matter wave associated with this particle is analogous to a wave on a string of length L that is fixed at both ends. Using the de Broglie relationship, show that (a) the quantized values of the linear momentum of the particle are

and (b) the allowed energies of the particle are

Transcribed Image Text:

nh п %3 1,2, 3, ... Ри п 2L 2L E, n- 8mL2 n = 1,2, 3, ...