In quantum mechanics, particles can be represented by complex-valued waves whose amplitudes correrspond to the probability of find the particle at that location. The dynamics of these wave function can be calculated from the famed Schrodinger wave equation -- the Newton's Law of quantum mechanics.
Numerical simulations based on the 1D Schrodinger equation were done on some paradigms of quantum mechanics and are shown below in MPEG format.
Scattering of particles is a good example of the probabilistic nature of quantum mechanics. In classical mechanics, a particle that meets another particle either passes by or reflects back, depending on the exact way the particles approach each other. In quantum mechanics, the particle has probabilities of passing by OR reflecting back.
Click to see the small(180K)/ large(350K) version of a scattering movie, in which a moving particle -- the wave packet, is being scattered by a stationary particle -- the square well. Also, click on these to see the real and imaginary parts of the wavefunction are shown separately.
(Note that some insignificant boundary effects appear near the end of these movies)
Tunneling is an interesting and very unintuitive result that is uniquely quantum mechanical. It states that it is quite possible for a particle to pass right through a wall!! This result, forbidden by classical mechanics, is very very true!
Click to see the small(180K)/ large(350K) version of a tunneling movie, in which a moving particle -- the wave packet, partially tunnels through a wall -- the square barrier. And, click here to see the real and imaginary parts of the wavefunction are shown separately.
(Boundary effects appear in these as well)
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