Principles of Quantum Mechanics · Problem 5.4.1

The Harmonic Oscillator — R. Shankar

Physics — Quantum Mechanics · step-potential-transmission-coefficient

Problem

(Quite Hard). Evaluate the third piece in Eq. (5.4.16) and compare the resulting

T

with Eq. (5.4.21). [Hint: Expand the factor

(k_1^2 - 2mV_0/\hbar^2)^{1/2}

near

k_1 = k_0

, keeping just the first derivative in the Taylor series.]