How many particles have momentum in a specific interval?

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Homework Help Overview

The discussion revolves around a quantum mechanics problem involving a pulse containing α particles and their momentum within a specified interval. The original poster seeks to understand how to determine the number of particles with momentum in the range defined by the inequality 0 < hk < hk_0.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to clarify the meaning of the problem, questioning whether calculating the expectation value is necessary. Some participants suggest focusing on the probability of a particle having momentum within the specified range rather than calculating an expectation value.

Discussion Status

The discussion includes attempts to interpret the problem and clarify the requirements for finding the number of particles with specific momentum. Some guidance has been offered regarding the calculation of probabilities, but there is no explicit consensus on the approach to take.

Contextual Notes

The original poster mentions a specific reference to a textbook, indicating that the problem is part of a structured learning exercise. There is a noted lack of clarity regarding the expectations of the problem, particularly in terms of the calculations required.

najima
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Homework Statement



a pulse 1 m long contains 1000 α particles.at t=0,each α particles in the state

ψ(x,0){1/10e^(-ik_0 ) lxl≤50cm,k_0=π/50 and 0 for elsewhere,}
at t=0 ,how many particle s have momentume in the interval 0<hk<hk_0?

Homework Equations


introduction to quantum mechanics by liboff chapter 5/problems 4


The Attempt at a Solution

I don't understand what does it mean! I think I have to calculate expectation value?am I right?
 
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Expectation value of what? You are asked for the number of particles within a certain range of momenta. Since you know there are 1000 particles it would be sufficient to determine the percentage within that range. Looks to me like you want to calculate the probability a given particle has that momentum.
 


I can't get the answer ,please, help more.:-(
 


oh !finally I got! thax man!
 

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