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Some basics of Quantum mechanics
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Difference between quantum and classical mechanics, wave function, probability function, Linearity and superposition principal, quantum operators
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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 macroscopic Quantum mechanics describe motion of a
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 called
Energy is obtained or emmited continuously.
quanta.
Fails to explain energy matter equation. Successfully explain energy matter 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)
Quantum physics 1
, = (a)² - (ib)² = (a)²+(b)²
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
Quantum physics 2
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