What is the relationship between phi(r,t) and the given wave functions?

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Homework Help Overview

The discussion revolves around the relationship between a given wave function phi(r,0) and its time-dependent form phi(r,t). The context is within quantum mechanics, specifically dealing with wave functions and their evolution over time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the introduction of a phase constant in the time evolution of the wave function. Questions arise regarding whether modifications to the individual wave functions phi1 and phi2 are necessary. There is also discussion about applying energy values to these wave functions and how to incorporate them into the time-dependent equation.

Discussion Status

Some participants have provided guidance on how to proceed with the time evolution of the wave functions, suggesting that multiplying each wave function by an exponential factor related to energy is a viable approach. However, there remains a lack of explicit consensus on the exact modifications needed for phi1 and phi2.

Contextual Notes

There is mention of the Bohr radius as a relevant parameter in the wave functions, and the discussion includes the need for clarification on the application of energy values previously calculated for the wave functions.

Lee
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Homework Statement


phi(r,0)=1/rt(2)(phi1+ph2)

What is phi(r,t)?

Homework Equations


The Attempt at a Solution



Is this simply a case of introducing a phase constant to the eqn. So:

phi(r,t)=1/rt(2)(phi1+phi2)e^i(theta)t

or do we need to modify phi1 and phi2.
 
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phi1 exp(-iE_1 t/hbar)+ same for 2.
 
Oh, sorry.

phi1=Aexp(-r/ao)
phi2=B(1-r/ao)e(-r/2ao)

where ao is the Bohr radius.

As given by the question.

So can I take the Energy of each wave function (that I have already calculated) and apply the above substitution?
 
Can any give me some clarification.
 
Lee said:
Oh, sorry.

phi1=Aexp(-r/ao)
phi2=B(1-r/ao)e(-r/2ao)

where ao is the Bohr radius.

As given by the question.

So can I take the Energy of each wave function (that I have already calculated) and apply the above substitution?
Yes, just multiply each phi by exp{-iEt/hbar} and add.
 

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