Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Need some help with a proof

  1. Apr 14, 2005 #1
    from Griffith's, problem 9.15: Suppose Ae^iax + Be^ibx = Ce^icx, for some nonzero constants A, B, C, a, b, c, and for all x. Prove that a = b = c and A + B = C

    I'm definitely confused on where to begin my manipulation. It seems quite reasonable to meet that the constants should be equal, and the amplitudes should sum up to C but I dont know how to get there mathematically.

    Can someone give me a hint to get me started?
     
  2. jcsd
  3. Apr 14, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    HINT:make x=0.

    Daniel.
     
  4. Apr 14, 2005 #3
    if I make x = 0 then the relation a=b=c need not hold.

    By this I mean that e^n*0 = 1 for all n, hence a, b, and c can be any real number.

    So basically I'd trade proving a=b=c for A+B=C
     
  5. Apr 14, 2005 #4
    ok so wait.... I can use x = 0 to prove A+B=C (I did it by contradiction ie assume A+B != C for all x. then insert x=0 and you get A+B=C - a contradiction).

    then can I use the fact that A+B = C to prove that a=b=c?
     
  6. Apr 14, 2005 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Nope.That x=0 will probe that A+B=C.Now u'll have to make use of the independence of the [itex] e^{ix}[/itex] and [itex] e^{x} [/itex] for [itex] x\in \mathbb {R} [/itex].

    Daniel.
     
  7. Apr 14, 2005 #6
    I'm sorry but I dont understand what you mean by the independence of e^ix and e^x.
     
  8. Apr 14, 2005 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    [tex] Ae^{ix}+Be^{x}=0\Leftrightarrow A=B=0 [/tex]


    Daniel.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook