Need of Wave Packet: Schrodinger's Postulate

[roshan2004]

Why Schrödinger postulated that a material particle in motion is equivalent to a wave packet rather than a single wave train?

 

[SpectraCat]

Why Schrödinger postulated that a material particle in motion is equivalent to a wave packet rather than a single wave train?

By "a single wave train" I guess you mean a plane-polarized wave with a perfectly precise wave vector, e.g.:

$$\phi\left(x\right) = e^{ikx}$$

The problem with this function is that it has infinite extent, or infinite uncertainty in position space, as required by the HUP, since $$\Delta p = 0$$ for this choice. That means that the function is not square-integrable, and therefore is not normalizable, and cannot represent a wavefunction that is a solution the Schrödinger equation.

 

[roshan2004]

I am new to quantum mechanics and have just started introductory wave mechanics so can u please explain it to me in simple terms

 

[Claude Bile]

Some of this expands on Spectracats post;

A wave-packet is a function that is spatially localised, whereas infinite wave trains continue to the ends of the universe. When we look at an experiment (single-slit diffraction for example), we know that the electrons are spatially localised in some fashion (within the lab, for example), thus we need a wave-packet to describe the position of the particle.

Since wave-functions represent probability, thus they are mathematically constrained in that the integral over all space must = 1. To be normalisable, the integral over all space must be finite. Wave-packets possesses this property, but single wave trains do not.

Claude.