Probability density — UPSC Physics Optional CSE 2024 Paper II

The ground state wave function of a harmonic oscillator is \psi_0(x) = \left(\frac{m\omega}{\hbar \pi}\right)^{1/4} \exp\left(-\frac{m\omega x^2}{2\hbar}\right). (i) At which point is the probability density maximum ? (ii) What is the value of the maximum probability density ?