Probability Amplitude Homework: Showing Definition of Time Derivative

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Homework Help Overview

The problem involves demonstrating a relationship involving the time derivative of a probability amplitude, specifically showing that the time derivative of the inner product of two states can be expressed in terms of the time derivatives of each state. The subject area pertains to quantum mechanics and the mathematical treatment of wave functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants express uncertainty about how to begin the problem and seek guidance on the initial steps. There is mention of the potential relevance of calculus and the product rule in the context of the time derivative. Questions arise regarding the definition of the inner product of the states involved.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. Some have suggested that the question may not be as complex as initially thought, while others are seeking clarification on definitions and relevant equations. No consensus has been reached yet.

Contextual Notes

There is a lack of explicit definitions provided in the original problem statement, which may affect the clarity of the discussion. Participants are navigating assumptions about the nature of the wave function and the relevant mathematical principles.

teme92
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Homework Statement


Show, using the definition, that ##\frac{d}{dt}\langle \emptyset(t)|\psi(t)\rangle=\langle \frac{d}{dt}\emptyset(t)|\psi(t)\rangle+\langle \emptyset(t)|\frac{d}{dt}\psi(t)\rangle##

Homework Equations

The Attempt at a Solution


I'm looking at this and I have no idea where to begin. Could someone please help me with how I'm supposed to start this. Any help would be much appreciated.
 
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The (unstated) definition i question likely provides one of the relevant equations. Beyond that, it looks like a bit of calculus.
 
It doesn't state what the definition is but based on the ##\psi(t)## I'd guess its somthing to do with the wave function. I'm thinking that the question isn't as complicated as I thought and its just the product rule.
 
What is the definition of ##\left< \phi \left(x,t\right) | \psi \left(x,t\right) \right>##?
 
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Hi George I found a solution to the problem, thanks for the help.
 

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