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Quantum Mechanics (Wave Functions and the One Dimensional Schrodinger'…
Quantum Mechanics
Wave Functions and the One Dimensional Schrodinger's Equation
Used a wave for mechanics,sound,EM. Now we extend this to Quantum
For mechanical waves just knowing time and position gave us a function that can describe a wave in its entirety y(x,t)
In Quantum we have \(\Psi\)(x,y,z,t)
Interpretation of the equation
EM interpretation
The intensity for constructive and destructive interference is proportional to the square of the E field
Photon interpretation
The intensity for interference represents the probability that a photon will strike around a point
Similarly the wave function squared is proportional to the probability that a photon will hit a point
Technically absolute value of \(|\Psi | \)
Uncertainty
Momentum= a constant
\(p=\hslash k\)
This means we know momentum (there is no uncertainty)
if \(\Delta p=0\) then \(\Delta x=\infty\)
This means we don't know where on the x axis the particle is
Energy
Energy= constant
\(\Delta E=0\) so \(\Delta t=\infty\)
We know energy which means we don't know
when
a particle passes a point
Introduction
Quantum Mechanics is the study of particles exclusively as waves
Schrodinger's equation for Quantum mechanics is what Newton's Laws are for Mechanical Physics or Maxwell is to EM