# Homework Help: Interpretation of Quantum Mechanics

1. Mar 18, 2014

### mimocs

I want to ask you guys about the interpretation of Quantum Mechanics.

I am using Griffiths' Introduction To Quantum Mechanics as a textbook.

In this book, on chapter 1.3, there is an explanation about 3 different views of quantum mechanics, realistic, orthodox, agnostic.

My homework question is
Explain the followings briefly, based on the realist, orthodox, and agnostic positions respectively.
1. Where was the particle just before the measurement?
2. What happens if we made a second measurement immediately after the first?
3. What would be the probability distribution for an ensemble of states prepared with the same initial condition? Compare the three positions.

My problem is on the third question.
1 and 2 is just on the textbook so I have no problem with them.

However 3, I am not very sure.

In my opinion, answer is this.
realistic : Probability distribution looks like a delta function since the states are all the same.
orthodox : Probability distribution will be widely.

I actually have no logic for the answers.

2. Mar 19, 2014

### vanhees71

This is, in fact, not a physics but a philosophy question. The answers depend on what your point of view concerning the interpretation is. It starts with the very subjective meaning of the word "realistic". I'm a follower of the minimal statistical interpretation which tries to only use the minimum of metaphysical ideas to apply the quantum-theory formalism to interpret observations in the lab. For me that's the most "realistic" interpretation, but some people have another understanding of "realistic" and call this point of view a non-realistic interpretation.

The only point that's independent of interpretation is 3) and that's why I can answer this question within the minimal statistical interpretation. The probability distribution to measure a certain value $a$ of the observable $A$ is given by
$$P(a|R)=\sum_j \langle a,j|\hat{R}|a,j \rangle.$$
Here $|a,j \rangle$ is a complete set of eigenvectors of the operator $\hat{A}$ that represents the observable $A$ for the eigenvalue $a$ and $\hat{R}$ is the statistical operator due to the preparation of the system in the corresponding state.