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Wave functions 
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#1
Sep1810, 01:51 PM

#2
Sep1810, 02:18 PM

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PF Gold
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If k_{1}=k_{2}, the strings are identical, and you get no reflection.
Your wave function in region 1 looks a bit off. Typically, the second term is B e^{i(k1+ωt)}. That still describes a wave moving to the left, but it lets the time dependence cancel out of the equations. Plus it'll result in equations you can actually solve. 


#3
Sep1810, 02:23 PM

P: 677

But your conclusion is that there's a mistake in the question? 


#4
Sep1910, 03:32 AM

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Wave functions
Sorry, that was a typo. There should be an x in there.
It appears there's a mistake in the question. You either get k1=k2, which means there should be no reflection, or C=0, which means there's no transmission. 


#5
Sep1910, 05:29 AM

P: 677

I've send an email to the instructor. Thanks for your help so far.



#6
Sep2010, 05:23 AM

P: 677

The instructor repied back there isn't any mistake in the exercise, it is possible! But I don't know how!



#7
Sep2010, 03:14 PM

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Well, if you take the problem as given, the only consistent solution I see is B/A=0 and C/A=1, which in turn requires k1=k2. I've asked others to take a look at this thread. Perhaps they'll spot something we're both overlooking.



#8
Sep2010, 03:28 PM

P: 677

The instructor gave the answer if you take the real part of both equations you'll get a set of 2 equations which indeed lead to the right answer.



#9
Sep2010, 03:32 PM

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PF Gold
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#10
Sep2010, 03:39 PM

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#11
Sep2010, 03:42 PM

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If on the other hand [itex]y_1=Ae^{i(k_1x\omega t)}+Be^{i(k_1x+\omega t)}[/itex] , you don't have that problem, and there is a sensible solution. 


#12
Sep2010, 08:22 PM

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ehild 


#13
Sep2110, 05:24 AM

P: 677

He told us that the real part has a physical meaning therefore only the real part of the functions have to be considered. But I don't get what you mean by the typo. The imaginary part of the function is irrelevant, isn't it?



#14
Sep2110, 05:31 AM

P: 677




#15
Sep2110, 10:03 AM

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If, on the other hand, you choose your complex waverfunction so that both imaginary and real parts can satisfy the boundary conditions, you are free to do all the calculations with the complex wavefunctions and then simply take the real part at the very end to get your physical result. 


#16
Sep2110, 10:16 AM

P: 677




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