Quantum Mechanics Expectation

In summary, the conversation discusses the calculation of the expectation values for the momentum and position of a particle trapped in a one-dimensional box. The equations <p_{x}> and <x> are used, along with the wavefunction Ψ, to find these values. The boundaries of the box, x=0 and x=L, are used as the limits for the integrations.
  • #1
roshan2004
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Quantum Mechanics "Expectation"

Homework Statement


1. Calculate the expectation value [tex]<p_{x}>[/tex] of the momentum of a particle trapped in a one-dimensional box.
2. Find the expectation value <x> of the position of a particle trapped in a box L wide.

Homework Equations


[tex]\psi _{n}=\sqrt{\frac{2}{L}}sin \frac{n\pi x}{L}[/tex]
[tex]<p_{x}>=\int \psi^*p_{x}\psi dx[/tex]
[tex]<x>=\int \psi^*x\psi dx[/tex]

The Attempt at a Solution


I got confused on choosing the limits for both the problems for integrating them. What's the limits I should chose for both the problems.
 
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  • #2


Where is Ψ non-zero? (What are the boundaries of the box?)
 
  • #3


x=0 and x=L
 
  • #4


Thanks I got it. The limits that I have to use are x=0 and x=L
 
  • #5


Exactly. :wink:
 

1. What is the concept of expectation in quantum mechanics?

In quantum mechanics, expectation refers to the predicted outcome of a measurement or observation of a quantum system. It is calculated by taking the average value of the possible outcomes weighted by their respective probabilities.

2. How is the expectation value related to probability in quantum mechanics?

The expectation value is directly related to the probability of a certain outcome in quantum mechanics. It represents the most likely value that will be obtained in a measurement, based on the probabilities of all possible outcomes.

3. Can the expectation value be greater than the maximum possible value in quantum mechanics?

No, the expectation value cannot be greater than the maximum possible value in quantum mechanics. This is because the expectation value is calculated using the probabilities of all possible outcomes, and any value that exceeds the maximum possible value would have a probability of 0.

4. How is the concept of expectation used in the Schrödinger equation?

The Schrödinger equation, which describes the time evolution of a quantum system, includes the expectation value as a key component. It is used to calculate the expected future state of a quantum system, based on the current state and the Hamiltonian operator.

5. Can the expectation value be used to determine the exact outcome of a measurement in quantum mechanics?

No, the expectation value cannot determine the exact outcome of a measurement in quantum mechanics. It can only provide a prediction of the most likely outcome, as the actual outcome of a measurement is determined by the inherent randomness of quantum systems.

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