Quantum mechanics: how to sketch the wave function?

[Fatimah od]

Homework Statement

Homework Equations

The solution which I found:

http://www.lamst-a.net/upfiles/mRA51397.png

The Attempt at a Solution

I tried to solve part (a)

http://www.lamst-a.net/upfiles/wFU51621.jpg

Please explain it to me.

 

[voko]

I don't see how the solution you found corresponds to the problem.

Your solution is incorrect because you ignore the function in [0, a].

 

[Fatimah od]

so should i do the same integrate with the both intervales ?

 

[voko]

Compute the integral over the entire range [0, b]. Equate the result with 1 and solve it for A.

 

[Fatimah od]

http://im26.gulfup.com/2012-09-13/1347559112201.jpg

how is it now !

 

[voko]

I do not see any difference from the previous attempt. You are still not taking the entire [0, b] range.

 

[Fatimah od]

sorry I upload the wrong pic.

hear is the whole range.

http://im24.gulfup.com/2012-09-13/1347562820501.jpg I hope that I'm doing well.

 

[voko]

This seems OK.

 

[vela]

Please make your images smaller or simply link to them. When they're large, like yours, it makes it hard to read the thread.

 

[Fatimah od]

fine,, thanx

so how should I sketch the function now ?!

help me please ,

 

[vela]

Put to use what you learned in your algebra classes and plot the function.

 

[Fatimah od]

Iam trying ,,
is the time on the (x-axis)
and the position on the (y-axis) ?

should I write two tabels for the both cases individual !

 

[voko]

You are asked to sketch the function at t = 0 as a function of x.

 

[Fatimah od]

while i asked to sketch at t=0 , so i will use the first function ..

http://im18.gulfup.com/2012-09-13/1347568161121.jpg

i Supposed a random numbers ,,

how is it ?!

 

[voko]

You need to sketch this on the interval [0, b]. With a somewhere in between. Random numbers are useless.

 

[Fatimah od]

sorry
can you explain more please ,,
how could I draw without a points !

 

[voko]

On the x axis, choose some interval. Label its left end "0", its right end "b". Somewhere in that interval, choose another point, label it "a". What are the values of the function at those three points? Put them on them on the diagram. What else do you need to complete the sketch?

 

[Fatimah od]

how to chose the values of the position,which located on the y-axis ?

 

[voko]

I do not understand the question.

 

[Fatimah od]

I am trying to say that ,,
if the time will label on the x-axis with 3 points (0,a,b)
what is the functions which should label on the y-axis ?

 

[voko]

As I already said, there is no time in this problem. As to what labels you should use on the y axis, consider what values you are going to plot.

 

[Fatimah od]

i'm keep trying , but I do not know why I did n't catch the idea !

is this right ?

http://www.gulfup.com/show/X356ozhua4h0kks

 

[voko]

What are the values of the function at 0, a and b?

 

[Fatimah od]

ψ = Ax/a
ψ = A (b-x)/(b-a)

i know that it's not available to put an (a variable) as a point ,,
that it's why I want to suppose a value for "a" and "b" !

 

[voko]

Those are not values of the function. Those are the function itself.

 

[Fatimah od]

huh ,, I confused !
would you like to draw an example ,, please !

 

[voko]

What is the value when x = 0? When x = a? When x = b?

 

[Fatimah od]

i think it's correct now ,,

http://www.gulfup.com/show/X9fk6ltca3fwoco

^
^
i hope ()

 

[voko]

No, that's not correct. You have one function, not two.

You have INTEGRATED the function over [0, b]. But you are unable to compute values of the same function in three points in the same interval. How is this possible?

 

[Fatimah od]

but the function is divided in the two interval , so how can I compute one function
I'm forced to express the function as two parts, I thought !

 

[voko]

Your function has ONE value at any ONE point x. Not two, not three, not any other number.

 

[Fatimah od]

you mean A=√3/b ?

 

[voko]

At what point is that the value of the function?

 

[Fatimah od]

at "A" from the integrated

 

[Fatimah od]

all what I need to draw is the values which are on the y-axis
and that is to describe the wave function ψ

the problem now is " what is the function on (0,b)"?

I'm not sure if I can summate the two parts from (0,a) to (a,b) without any other operator such as "integral" ?

actually I think it's not correct two ,, it leads to a complicated formulas !
but that's what I could think about to get one function as what you said ,,, !

please ,
I need to more help ()