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

I Kets and vectors

  1. Jul 16, 2016 #1


    User Avatar

    Hi. I have read that when working in 3-D the following kets | x > and | p > are not vectors in 3-D. If that is correct what are they ? I know | ψ > is an abstract vector but I thought | x > and | p > would be 3-D vectors in the position and momentum representation ?
  2. jcsd
  3. Jul 16, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    They are vectors in an infinite-dimensional space. It is natural to feel that ##|x\rangle## should be in a 3d space because ##x##, without the enclosing symbols, is a coordinate in 3D space. But ##|x\rangle## is not a coordinate or any other type of number. In the position representation it is the Dirac delta function ##\delta_x##, which is an element of a space of functions, which - like most function spaces - is infinite-dimensional.
  4. Aug 3, 2016 #3
    <a is conjugate of a>
    <a|b> kind of dot(a.conjugate , b)
    b><b|a> projection into other direction like b*dot(b.conjugate , a)

    v2=pol><pol|v> is equivalent with this pseudo code
    v2.x = pol.x*amp
    v2.y = pol.y*amp

    conjugate of V is V.imaginary=-V.imaginary
  5. Aug 3, 2016 #4
    The Pauli matrices transform the 3d direction into 2d complex vector like spin.
  6. Aug 3, 2016 #5
    Why do we need conjugation?
    because there is a minus sign in real part of multiplication of complex numbers.

    complex operator *(complex c)
    complex e;
    e.real = this->real*c.real - this->img*c.img;
    e.img = this->img*c.real + this->real*c.img;
    return e;
  7. Aug 3, 2016 #6

    A. Neumaier

    User Avatar
    Science Advisor

    They are distributions, elements in the dual space of a Schwartz space of smooth functions. Only the labels are vectors in 3D.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Kets vectors Date
I Inner products and adjoint operators Apr 25, 2016
Ket Vectors Nov 5, 2015
Ket Vectors Oct 28, 2015
Why do ket vectors not have magnitudes? Mar 13, 2015
Composing three ket vectors Mar 6, 2013