Question

Find the function, f(x), for which  X f(x) = \(-\frac{i}{\hbar}a^2p_xf(x),\) where a is the real quantity.

(a) ke^-x^2

(b) ke^-x^2/2a

(c) ke^-x^2/2a^2

(d) ke^-x^2/2a

This question was posed to me in examination.

I want to ask this question from Schrodinger Equation (Time Dependent Form) topic in portion Quantum Physics of Engineering Physics I

Answer 1

Right answer is (c) ke^-x^2/2a^2

The best explanation: Now, given that, X f(x) = \(-\frac{i}{\hbar}a^2p_xf(x).\)

X f(x) = \(-\frac{i}{\hbar}a^2p_xf(x)/dx\)

df/f  = -xdx/a^2

ln f = -x^2/2a^2 + C

f = ke^-x^2/2a^2.