Do we need both the position and momentum vectors to know successive states of an electron's movement? Or is one sufficient?

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    $\begingroup$ Your title doesn't seem to match your question. Are you asking about what information is needed to specify the motion of an electron, or are you asking about the uncertainty principle? $\endgroup$ – enumaris Aug 10 '18 at 17:35
  • $\begingroup$ What information is needed to specify the motion sir that's what I want $\endgroup$ – sai sri datta Aug 10 '18 at 17:37
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    $\begingroup$ Are you assuming the Bohr model of the atom? Otherwise, there isn't one "position vector" or "momentum vector" for an electron in an orbital; it's delocalized throughout the orbital, with a wavefunction that can be represented either in position space or in momentum space. $\endgroup$ – probably_someone Aug 10 '18 at 17:43
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    $\begingroup$ Your question seems to imply that an electron in an orbital has a classical trajectory. It doesn't. $\endgroup$ – PM 2Ring Aug 10 '18 at 17:53
  • $\begingroup$ You've used the quantum mechanics tag, but there's a distinct answer only when considering a classical electron. With QM, you get a wavefunction and hence a probability of different positions/momentums. $\endgroup$ – Chair Aug 12 '18 at 3:23

An electron in an orbital is described by QM, so it doesn't make sense to talk about position vector or momentum vector. You can, however, calculate the mean values of the coordinates.

But, if you're looking for the description of its motion, it is all about wavefunctions. You need to know

  1. The initial state $\psi(t_0)$.
  2. The Hamiltonian $H$

Then, the "motion" (time evolution) is given by Schrödinger's equation.

$$ \frac{\partial}{\partial t} \psi = -\frac{i}{\hbar} H\psi $$


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