Probability for a particle in a box

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SUMMARY

The probability of finding a particle in a one-dimensional box of width 2a, described by the wave function \(\psi=\frac{1}{\sqrt{2a}}\) for \(|x| \leq a\), is calculated by integrating the wave function over the interval \([-b, b]\). The resulting probability is \(\frac{b}{a}\). For momentum calculations, the discussion highlights the need to understand the momentum operator and its eigenvalues, which are essential for determining possible momentum measurements.

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  • Quantum mechanics fundamentals
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  • Knowledge of the momentum operator in quantum mechanics
  • Familiarity with integration techniques in calculus
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Homework Statement


A particle in a box of width 2a is in a state \psi=\frac{1}{\sqrt{2a}} for |x| less than or equal to a and 0 for |x| greater than a. What is the probability of finding the particle in [-b, b] inside the box? What is the probability of finding the particle with momentum p inside the box?

Homework Equations


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The Attempt at a Solution


So, for the probability of finding the particle in [-b,b], I simply integrated the function from -b to b and found that the probability is b/a.

I'm not sure how to approach the probability calculation for finding the particle with momentum p though...can someone please provide some guidance?
 
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What measurement values of the momentum operator are possible?
 

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