Question

How the wave function and wave packets can be used to explain the particle-wave properties of electrons?

Answer 1

Interpretation of wavefunction was given by Scientist Born, termed as 'Born's Interpretation of a wavefunction'

This says, The basic connection between properties of wavefunction   and behaviour of associated particle is expressed in terms of probability density.

Probability density is the probability of finding the particle per unit length (say for the x coordinate) at time t is

we have defined the position of particle (in terms of probabilities) by using wavefunction and also the wavefunction is used for its wave properties.

To define its motion we use wavepackets.

To define the properties of electron being a wave is given by De Broglie interpretation, which said 'with every moving particle, there is associated a wave with wavelength called De Broglie wavelength'

Now definite wavelength means definite momentum   , and from uncertainty principle it cannot have definite position, and therefore to define the position of moving particle we superpose many waves of different wavelengths (called wavepacket) on the cost of losing information of its momentum.

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