I'm going through a textbook, on what is pretty much my first course in Quantum mechanics. I've got to a section were it says that in order for a sinusoidal wave function to correspond to a non infinite probability distribution, there must be a range of momentum, or at least more than 1 momentum term on x.. Which I understand, that makes complete sense. However the next bit they utilize an integral term to sum momentum over a unit step like distribution. That is they consider the wave function to be built up from an integral w.r.t momentum, composed of various sinusoidal terms. This integral considers momentum to be a continuous range.(adsbygoogle = window.adsbygoogle || []).push({});

Equation of concern (probably makes little sense): Ψ(x,t)=(2πħ)^-½ ∫ e^{i[px-Et]/ħ} *Φ(p) dp

However why isn't momentum quantized? Surely energy exists in steps related to h, which will extend to quantum's of momentum. Hence in a momentum range, a sum would be needed.

Am I wrong in thinking that momentum is quatized, or is it that the integral is a close match to the sum due to the size of h? The reason I'm annoyed at this is that they use this to relate wave function and momentum together in a Fourier transform manner. Which I presume is the basis for Heisenberg's uncertainty principle. I feel uneasy about leaving such a hole in my knowledge with the significance this derivation poses.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Continuous momentum range

**Physics Forums | Science Articles, Homework Help, Discussion**