Quantum Mechanics wavefuction collapse

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Homework Help Overview

The discussion revolves around a quantum mechanics problem involving a harmonic oscillator in its ground state. The problem presents a scenario where momentum is measured, and participants are tasked with determining the probability that the energy remains unchanged following this measurement.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the concept of wave function collapse and its implications for the state of the system after measurement. There are inquiries about how to calculate the wave function after the momentum measurement and the probability of remaining in the ground state.

Discussion Status

The discussion is active, with participants questioning the mechanics of wave function collapse and seeking clarification on how to approach the calculation of probabilities related to the energy state after measurement. Some guidance has been offered regarding the relationship between the ground state and the probability of unchanged energy.

Contextual Notes

Participants are navigating the complexities of quantum measurement and the implications of state changes, with specific focus on the harmonic oscillator model. There is an acknowledgment of the need for numerical methods to solve the problem, but details on constraints or specific homework rules are not provided.

sty2004
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Homework Statement


Consider a harmonic oscillator. It is in the ground state. Momentum is
measured and is found to be between 0.2 \sqrt{}m\omega hand 1.5 \sqrt{}m\omega h. (h here is h bar)
Energy is now immediately measured. What is the probability that the energy is
unchanged? You may want to do it numerically.



Homework Equations





The Attempt at a Solution


I don't know what to start with. Maybe P(E unchange)=|<\varphi0|wave after measurement>|2
 
Last edited:
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That's right. If the energy is unchanged, it's in the ground state, so you want to find the probability the oscillator is in the ground state after the momentum is measured.
 
how to find wave after measurement then?
 
Making a measurement causes the wave function to collapse. How does the collapse work in general?
 

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