Applied Physics I: Chapter 7: Quantum Mechanics
Physical significance of a wave function
Wave function: It is the variable quantity that is associated with a moving particle at any position (x, y, z) and at any time 't' and it relates the probability of finding the particle at that point and at that time.
PHYSICAL SIGNIFICANCE
OF A WAVE FUNCTION [ᴪ]
Wave function:
It is the variable quantity that is associated with a moving particle at any
position (x, y, z) and at any time 't'
and it relates the probability of finding the particle at that point and at
that time.
•
It relates the particle and the wave statistically
(i.e.,) ᴪ(x, y, z, t) = A e-iω( t - x/v )
(or) ᴪ = ᴪ e‒iωt
•
Wave function gives the information about the particle behaviour.
•
ᴪ is a complex quantity and individually it does not have any meaning.
•
|ᴪ|2= ᴪ*ᴪ is real and positive, it has physical meaning. This
concept is similar to light. In light, amplitude may be positive (or) negative
but the Intensity, which is the square of amplitude is real and is measurable.
•
|ᴪ|2 represents the probability density (or) probability of finding
the particle per unit volume.
•
For a given volume dτ, the probability of finding the particle is given by
Probability (P) = ∫∫∫ |ᴪ|2 dτ
where
dτ = dx.dy.dz
•
The probability will have any value between zero to one. (i.e.,)
(i)
If P=0 then there is no chance for finding the particle (i.e.,) there is no
particle, within the given limits.
(ii)
If P=1 then there is 100% chance for finding the particle (i.e.,) the particle
is definitely present, within the given limits.
(iii)
If P=0.7, then there is 70% chance for finding the particle and 30% there is no
chance for finding the particle, within the given limits.
Example: If
a particle is definitely present within a one dimensional box (x‒direction) of length ‘l’, then the probability of finding the
particle can be written as
P=0∫1
|ᴪ|2 dx = 1
Applied Physics I: Chapter 7: Quantum Mechanics : Tag: Applied Physics : - Physical significance of a wave function
Applied Physics I: Chapter 7: Quantum Mechanics
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