Question

So the solution i have so far is what i got from an online solution, but i still dont fully understand how to get the general solution for this problem (the part highlighted in pink). Can someone go into depth as to how to get the general solutions for each of the regions.

-Lacas)5C- Problem a a7) Consider the double delta-function potential Nexo L &and a are positiNe Ca Sketch the potenttial VCx VCO= -a 8x) -a (b) How many bound states does it possess Find tne atlowed energiesfor a= ma and for 4ma The Schrödwger equation for the double delta function Ycx) = E 4cx) am d YCx) 2ME L M mass af the particie E IS tne enerqy of the particle X= 1a, the schrödinger equatian becomes For 2mE x -mE E<O, Let Real and positive Since the probiem deals with bound States K ) dxYex The general even Solutions of the wave functions are, 4,02) Ae a Ia Apply baundary Conditions at Be Ce DX<a LAea =BeKa ceka Be Aex Ce -a< <o A-B Cea -a A-B(I+ e) Apply 4CK) IS Continuaus where Vcx)_is _finite the Condition that dx K(-B C)-(B-c) KBe B-C -2B = -2C - The general then becorne even soutions = B(1+ eka) ek* 7 a -as a BI e ) a =

Answer 1

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