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

B Wave equation, psi with dots and things like that...

  1. Dec 29, 2017 #1
    Hi everyone! I'm a psychologist form Brazil, so sorry for the bad English and for the lack of knowledge in math!

    I ve been trying to understand the Schrodinger equation and, as predicted, it's very hard!

    Please, help me with this:

    A sine wave function can be written as:

    F (x) = sin (x)

    And that can be represented as psi.

    The the derivative of that function can be written as:

    F (x) = cos (x)

    And that can be represented as psi dot.

    Also, the derivative of psi dot can be written as:

    F (x) = - sin (x)

    And thats psi with two dots.

    So far I understood!

    But things get confusing here:

    A wave equation can be written as:

    F (x) = A sin (2π f x )

    Where A stands for the amplitude, 2π f x stands for the period.

    But, in this video:



    It is stated, at 8 mins, that the correct wave function is, as expected:

    F (x)= sin (2π f t)

    And that's represented by psi

    But the derivative of that is

    F (x) = 2π f cos (2π f t)

    And not

    F (x) = cos (2π f t)

    (And that's represented by psi dot)

    To make things worst, the derivative of that last equation, psi dot, is represented by

    ## f (x) = - (2π f)^2 sin (2π f t) ##

    And not just

    F (x) = - sin (2π f t)

    (And that's represented by psi with 2 dots)

    Why is that?

    Thanks a lot!
     
  2. jcsd
  3. Dec 29, 2017 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    @Joao you need a calculus course.

    Dots above a function normally denote a time derivative. The normal convention for a derivative is either ##f'## or ##\frac{df}{dx}##.

    Then, of course, you have "partial" derivatives ##\frac{\partial \psi}{\partial x}## and ##\frac{\partial \psi}{\partial t}## etc.

    In answer to your question, there is a little thing called the chain rule, which is quite important!
     
  4. Dec 29, 2017 #3

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  5. Dec 29, 2017 #4
    Thanks a lot! I will do that! So, that makes sense, the derivative of

    Ψ = Sin (2πft)
    Is
    Ψ(dot) = 2πf cos (2πft)
    And not
    Ψ(dot) = cos (2πft)

    And after I make the calculus course, I will understand why?

    Really sorry to bother!
     
  6. Dec 29, 2017 #5

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes. You could, say, draw a graph of ##\sin(2x)## and look at the slope. You'll see that it is steeper than the graph of ##\sin(x)##.

    In fact, it's twice as steep at each point ##x##.

    Which is what you get from the chain rule.
     
  7. Dec 29, 2017 #6

    Thanks a lot for your time! I'll do the calculus course! =)))))

    Happy 2018!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Wave equation, psi with dots and things like that...
  1. Waves Equation (Replies: 2)

  2. Wave equation (Replies: 8)

  3. Wave equation (Replies: 4)

Loading...