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

This will give you the time-dependent Schrödinger equation for a particle in a box.In summary, the conversation discusses how to modify the wave functions phi1 and phi2, given the initial condition phi(r,0) = 1/√(2)(phi1 + phi2), to find phi(r,t). It is determined that the energy of each wave function can be multiplied by exp(-iEt/hbar) and added together to find the time-dependent Schrödinger equation for a particle in a box.
  • #1
Lee
56
0

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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  • #2
phi1 exp(-iE_1 t/hbar)+ same for 2.
 
  • #3
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?
 
  • #4
Can any give me some clarification.
 
  • #5
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.
 

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

1. What is a wave function?

A wave function is a mathematical representation of the state of a quantum mechanical system, such as an electron. It describes the probability of finding the system in a particular state at a specific time.

2. What does the wave function of an electron tell us?

The wave function of an electron tells us about its position, momentum, energy, and other physical properties. It also provides information about the probability of finding the electron in a particular location or state.

3. How is the wave function of an electron determined?

The wave function of an electron is determined by solving the Schrödinger equation, which is a fundamental equation in quantum mechanics. This equation takes into account the electron's energy, potential energy, and other physical properties to describe its behavior.

4. Can the wave function of an electron be directly observed?

No, the wave function of an electron cannot be directly observed. It is a mathematical concept used to describe the behavior of a quantum mechanical system. However, the effects of the wave function can be observed through experiments and measurements.

5. How does the wave function of an electron change over time?

The wave function of an electron changes over time according to the laws of quantum mechanics. It can be affected by external factors such as electric and magnetic fields, as well as interactions with other particles. The change in the wave function can also be described by the Schrödinger equation.

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