Foundations of Quantum Mechanics — UPSC Physics Optional CSE 2026 Paper II

A particle is in the normalized state \psi which is a superposition of the energy eigenstates \psi_1 and \psi_2 with energies 10\text{ eV} and 30\text{ eV}, respectively. The average value of the energy of the particle in the state \psi is 24\text{ eV}. Find the state \psi in terms of \psi_1 and \psi_2.