Quantum mechanics and expectation values.

In summary, quantum mechanics is a branch of physics that studies the behavior of matter and energy at a very small scale. It uses expectation values, which are average values of physical quantities, to make predictions about the behavior of quantum systems. These values are significant in understanding the probabilistic nature of particles at a subatomic level and are calculated using the wave function. While they can be measured in experiments, the measured value may not always match the expected value precisely.
  • #1
Rabbot
2
0
I have a question about expectation values in quantum mechanics.

Since calculating <x>=[itex]\int\Psi*x\Psi[/itex] does x always make this functions odd? If [itex]\Psi[/itex] is odd then [itex]\Psi*[/itex] I would assume is odd as well and then <x> would be odd*odd*odd, if [itex]\Psi[/itex] is even then I again assume it would be even*odd*even. Does an odd function make the whole function odd regardless of the two even functions?
 
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  • #2
Yup, if the wave function is even or odd, the integrand will be odd, so the expectation value will be 0.
 

1. What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It explains how these particles interact with each other and how they behave in different situations.

2. What are expectation values in quantum mechanics?

Expectation values in quantum mechanics are the average values of a physical quantity, such as position or momentum, that we can expect to measure in a large number of identical experiments. They are used to predict the behavior of quantum systems and are essential in determining the behavior of particles at a subatomic level.

3. What is the significance of expectation values in quantum mechanics?

Expectation values are significant in quantum mechanics because they allow us to make predictions about the behavior of quantum systems, which are inherently probabilistic in nature. They provide a way to determine the most likely outcome of a measurement and can help us understand the behavior of particles at a subatomic level.

4. How are expectation values calculated in quantum mechanics?

In quantum mechanics, expectation values are calculated using the wave function, which describes the probability of finding a particle in a particular state. The expectation value is then obtained by integrating the product of the wave function and the operator corresponding to the physical quantity of interest.

5. Can expectation values be measured in experiments?

Although expectation values are theoretical concepts, they can be measured in experiments. This is because the probability distribution described by the wave function can be experimentally determined, and the expectation value is related to this distribution. However, due to the probabilistic nature of quantum mechanics, the measured value may not always match the expected value precisely.

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