1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Need some help with a proof
  1. Need some help (Replies: 13)

Loading...