Principles of Quantum Mechanics · Problem 10.3.4

Symmetries and Their Consequences — R. Shankar

Physics — Quantum Mechanics · identical-particles-box

Problem

Two identical particles of mass mm are in a one-dimensional box of length LL. Energy measurement of the system yields the value Esys=ℏ2π2/mL2E_{\text{sys}} = \hbar^2\pi^2/mL^2. Write down the state vector of the system. Repeat for Esys=5ℏ2π2/2mL2E_{\text{sys}} = 5\hbar^2\pi^2/2mL^2. (There are two possible vectors in this case.) You are not told if they are bosons or fermions. You may assume that the only degrees of freedom are orbital.

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