Which of the following statements is true? a) If single measurements on identica

Question

Which of the following statements is true?
a) If single measurements on identically prepared systems give identical results, the system is in the eigenfunction corresponding to the measured eigenvalue.
b) If a system is in a superposition state, a single measurement on identically prepared systems will always give the same result.
c) If a system is in a superposition state, a single measurement on identically prepared systems will give any one of the possible eigenvalues with equal probability.
d) If a system is in an eigenstate of the operator corresponding to the property being measured, successive measurements on the system will give identical results.

Answer Choices:
B and D
B and C
A and D

Explanation / Answer

Which of the following statements is true?

a) If single measurements on identically prepared systems give identical results, the system is in the eigenfunction corresponding to the measured eigenvalue. --> Correct, by definition, there is only one eigenfunction ( unique function) if the system is given the same result.

b) If a system is in a superposition state, a single measurement on identically prepared systems will always give the same result. --> False, if they are superpositionated, then there should eb multiple values for the same result, that is, it is not a unique value

c) If a system is in a superposition state, a single measurement on identically prepared systems will give any one of the possible eigenvalues with equal probability. False, will not be with equal probability

d) If a system is in an eigenstate of the operator corresponding to the property being measured, successive measurements on the system will give identical results. True, since it is the eigenfucntion, expect the same predictable values on further calculations

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