Quantum Mechanics - Free Particle

A free particle with initial kinetic energy E and de Broglie wavelength λ enters a region in which it has potential energy V. What is the particle’s new de Broglie wavelength?

A. λ(1 + E/V)
B. λ(1 − V/E)
C. λ(1− E/V)^{− 1}
D. λ(1 + V/E)^½
E. λ(1 − V/E)^{− ½}

(GR0177 #46)

Solution:

The initial kinetic energy of free particle:


De Broglie wavelength:


Energy of the particle when it enters the region:


So, its wavelength becomes:




Answer: E