8. Consider two pure ensembles A and B, of identical particles each in an unknow

Question

8. Consider two pure ensembles A and B, of identical particles each in an unknown potential. The wave functions of particles in ensembles A and B at t- 0 are given as: Note that | (z) and 2(x) are the ground state (n-1) and first excited state (n-2) eigenfunctions with energy eigenvalues Ei and E2, respectively. (x) and 2(z) are both entirely real and are shown in the figure below. Is there an experiment that can be used at t = 0 to distinguish the particles in ensemble A from the particles in ensemble B? Explain your reasoning.

Explanation / Answer

Ensemble interpretation is the experiment which can be used to distinguish the particles in ensemble A from the particles in ensemble B.

The Quantum Ensemble Interpretation states that the state vector applies to an ensemble of systems, not an individual system. In Ensemble interpretation, the wavefunction i.e. the quantum state describes the ensemble of similarly prepared ensembles, not an individual particle.

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