Quantum wavefunction (Question 1 (10 Marks)) — UPSC Physics Optional CSE 2024 Paper II

A particle limited to the x-axis has the wave function \phi(x) = bx^2 between x = 0 and x = 2; the wave function \phi(x) = 0 elsewhere. (i) Find the probability that the particle can be found between x = 1.0 and x = 1.5. (ii) Find the expectation value <x> of the particle position.