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Summary Some Basic of Quantum Mechanics
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Basics information on wave function ,Quantum Operators,Difference between quantum and classical mechanics,
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Quantum physicsQ.1 - Difference between quantum and classical physics
Classical physics Quantum physics
Baised on Newton's law of motion. Baised on schodinger’s wave equation.
Classical mechanics describe motion of a Quantum mechanics describe motion of a
macroscopic object. microscopic object.
Based on particle nature of object. Based on dual nature of object.
We can't measure anything with 100%
Everything can measurable with 100% accuracy.
measurable.
Two observation position and momentum can be
Position and momentum are uncertain.
measure simultaneously
Energy released in the packet form is
Energy is obtained or emitted continuously.
called quanta.
Successfully explain energy matter
Fails to explain energy matter equation.
equation.
Units kg , meter Units nm,Α°
Q.2-The wave function
The quantity with which quantum mechanics is concerned is the wave function ψ. it
is the wave function which changes when the “matter-wave propagates”.
However, the wave function ψ itself has no physical interpretation . But it is highly
significant in presence of the particle.
Calculation of |Ψ|² at a particular place at a particular time gives the probability of
finding the particle there at that time.
The probability of finding a photon within a given volume of the beam is
proportional to the square of the amplitude of the wave associated with this beam.
The wave function may be real or it may be a complex function. If it is complex,
then it may be expressed as , ψ = a + ib,where a, b belongs to R.Complex conjugate
of the wave function is given by ψ*= a – ib.
Αnd |ψ|² = ψ*ψ =(a+ib )(a-ib)
= (a)² - (ib)² = (a)²+(b)²
Quantum physics 1
, The probability P(r, t) dV to find a particle within a small volume dV around a
point in space with coordinate r at some instant
of time t is
where ψ(r, t) is the wave function associated with the particle .
The probability of finding a particle
somewhere in a volume V of space is
|ψ|² is proportional to probability density P of finding the particle described by ψ,
the integral of |ψ|² over all space must be finite because the particle must be present
somewhere in given space , if ψ is infinite the probability density P is also be infinite
which is not possible. it can't be negative and complex.
Ιf,
particle does not exist at all
Integral of |ψ|² over the given volume V has to be equal to the probability density
(P) rather than proportional to it.
Quantum physics 2
, In the case of
Here the probability |ψ|² is equal to probability P over given volume V which gives us 1
called normalization condition.The wave function which obeys this equation is said to be
normalized.
Every acceptable wave function can be normalized by multiplying it with an
appropriate constant
For a one-dimensional case, the probability of finding the particle in the arbitrary
interval a ≤ x ≤ b is
And,
Since, wave function associated with a particle or a system Once, we know everything
about the system.
Q.3 .Well behaved wave function
~ A well behaved wave function in quantum mechanics is the wave function which has a
physical significance. This also means that the wave function should be meaningful and
does not behave awkwardly in a given interval.
Some conditions of a well-behaved wave function ψ are:
Quantum physics 3
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