Pupil Post by Saxon
Quantum mechanics is the study of particles and how they interact and behave. The main experiment from which quantum mechanics originated was the double slit experiment. The experiment was that an electron gun fired electrons onto a wall with two holes in it and onto a detector. When one slit was open the pattern on the detector gradually peaked at the point directly behind the open slit and the same thing happened when only the other slit was open. So you’d expect the pattern for both slits open to be the combination of the first two experiments. However, instead the pattern was going up and down periodically through the detector. This means that the particles were acting as waves and that the bumps were caused by the waves interfering with each other.
This phenomenon can be described by Schrodinger’s equation as shown here.
The Uncertainty Principle
A good place to start with quantum mechanics would be the uncertainty principle which states that you can’t know both the position and velocity of a particle. The math is as follows:
E = hf or energy = Planck’s constant × the frequency of a wave
So E = cp or energy = the speed of light × the momentum
This means that p = hf/c
We also know the equation c = the wavelength × the frequency
So f = c/the wavelength
This can be put into the other equation to get p = h/c × c/the wavelength = h/the wavelength (because the speed of light cancels out.)
If you want to accurately measure the position the wavelength <Δx
But if the wavelength is small then the momentum is large which means that it will give the particle a kick which would mean that you can no longer accurately know its speed.
How Quantum Mechanics Differs from Classical Mechanics
In classical mechanics or Newtonian physics you can measure the pace of states by using sets. A set is a single point on an axis. These sets can be put into groups and various other things but nothing else. However, in quantum mechanics sets can’t be used but are replaced by vector spaces over any complex number. The common notation for vectors is: Ia>.This is known as a Ket vector or Dirac notation.
These vectors can be multiplied: αIa> = Ib>
They can also be added: Ia> + Ib> = Ic>
And both: αIa> + βIb> = Ic>
If you were to open them they’d be like this: Ψ(x) = ΨR(x) + iΨI(x)
“R” being the real part and “I” being the imaginary part.
For every complex number there is a complex conjugate represented as <aI that goes with it as shown by this graph.
Physical Significance of Vectors in Quantum Mechanics
Say you tossed a coin (or measured the spin of a particle), in classical mechanics you could only have either heads or tails. However, in quantum mechanics you can have both heads and tails or a bit of both. This is due to the vectors because they can be added and multiplied in the way that their values won’t be certain until looked at and once that occurs they could have a completely different or unusual value. This is the very basics of quantum mechanics which can explain phenomena such as quantum entanglement or QED.
Part two will be written once I finish my scholarship and will include things like basis vectors, linear operators and matrix elements.
Questions (added by HCTR)…
- What property of light is governed by wavelength?
- If the frequency of a musical note doubles, what musical change occurs to the pitch?
- What can you say about the acceleration of an object that only has balanced forces acting upon it?
- What can you say about the forces acting on a skydiver who is accelerating towards the ground?
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