Measuring Energy of Mass and Spring System

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Homework Help Overview

The problem involves a mass connected to a spring, exploring the energy dynamics when a stop restricting motion is suddenly removed. The context is within the framework of simple harmonic motion, focusing on energy measurements in a quantum mechanical setting.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss defining the potential energy of the mass before and after the stop is removed. There are inquiries about relevant equations and the initial conditions of the system. One participant attempts to express the wave function in terms of a series expansion and questions the appropriate form of the wave function.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the setup and potential energy definitions. Some guidance has been offered regarding the potential energy landscape, but there is no explicit consensus on the next steps or methods to approach the problem.

Contextual Notes

Participants are working under the constraints of a quantum mechanical interpretation of the system, with specific attention to the implications of the stop on the energy states. There is an emphasis on the need for initial attempts or equations to facilitate further discussion.

sty2004
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Homework Statement


A mass m is connected to a spring of spring constant k. The equilibrium
position is x = 0 and the motion of the mass m is restricted by a stop such that
spring compression is not allowed, i.e., x < 0 is forbidden . The
system is in the ground state.
(a) The stop is suddenly removed and the energy is immediately measured.
What is the probability that the energy remains unchanged?
(b) If energy is measured after some delay from the instant the stop is
removed, will your answer be different?


Homework Equations





The Attempt at a Solution

 
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Nice question.
What are your ideas so far? Any relevant equations?
If you want us to help you, you have to give us a starting point where to help.
 
Your first step is to define the potential of the mass before and after the stop is removed.

Picture the SHO (simple harmonic oscillator) potential which is a parabolic well and then the "stop" cuts this parabolic well in half.

That's as much help as I can give without seeing any attempt or work.
 
attempt:\Phi(x,0)=\sumcn\phin
and cn=<\phi|\Phi>
and then P=|c1|2=|<\phi|\Phi(x,0)>|2 ? what should be \phi ?
 

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