Solving the Wave Function: Find Ea, q, and Time?

The graph of the wave function (with respect to space) is a combination of a sine wave and a cosine wave.i) -------------------------------The slope down is called the potential well. The peak is called the barrier.ii) -------------------------------The first wave function is associated with a particle that is not bound by the potential well. The second wave function is associated with a particle that is bound by the potential well.In summary, the conversation discusses finding the equation for a question involving waves and wave functions that interfere constructively over a specific region. The solution involves time-dependent terms and a periodic time function, with the graph of the wave function being a combination of a sine and cosine wave. The
  • #1
squaric
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Homework Statement



http://img29.imageshack.us/img29/5236/phst.jpg

Homework Equations



http://img25.imageshack.us/img25/8815/11203939.jpg

I need to find the equation for the question.

The Attempt at a Solution



a)

A bunch of waves/wave functions, that have phases/amplitudes that interfere constructively.

b)

|Y(x,t)|Squared = Co(/)0 + C1(/)1 Squared ?

c)

No idea

d)
i)

A graph that slopes down, (qe) to then up to a peak, (Difference between each point is Ea) then finally back down to q.
ii)

Down then up then to a straight like across.
I'd also like to know how to work out the time taken to travel to an adjacent potential well assuming Y(x,t=0) = Co(/)0 + C1(/)1
I think (/)0 and (/)1 are the lowest eigenstates and C0 and C1 are just coefficients.

(I think the original thread was posted in the wrong section!)
 
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  • #2


The complete solution was deleted (it's not allowed). So if you didn't see it:

(a) ------------------------------

The waves must interfer constructively only over a region.

(b) ------------------------------

You have forgotten some time-dependent terms.

(c) ------------------------------

The correct solution of (b) contains a periodic time function. It's period is the answer
 

What is the wave function?

The wave function is a mathematical representation of a quantum system that describes the probability of finding a particle in a particular position or energy state.

What is Ea?

Ea, also known as the activation energy, is the minimum amount of energy required to initiate a chemical reaction. It is often represented as the difference in potential energy between the reactants and the transition state.

What is q?

Q, also known as the reaction quotient, is a ratio of the concentrations of the products and reactants in a chemical reaction at any given time. It is used to determine the direction in which a reaction will proceed.

What is time?

Time is a fundamental concept in physics that measures the duration of events and the intervals between them. In the context of solving the wave function, time is used to determine the rate at which a chemical reaction occurs.

How do you solve for Ea, q, and time?

To solve for Ea, q, and time, you will need to use mathematical equations and data from experiments to calculate these values. The specific steps and equations used will depend on the type of chemical reaction being studied and the available data.

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