QUANTUM PHYSICS!
The basic description of nature is
in terms of probability amplitudes or state functions ψ(r,
t) such that |ψ|2 is the probability that the system
is found at space-time point r, t.
Probability waves have f = E/h
and λ = h/p.
Knowledge of the position r
of a process destroys any information which might have existed
concerning the system's momentum p. Similarly knowledge
of the time at which a process occurs destroys information which
might have existed concerning the total energy of the process!
A particle or system with a
finite lifetime τ does not have a definite mass or energy,
because ΔMc2 ∼ ℏ/τ.
A particle of mass M can
appear out of nothing, if it vanishes back into nothing after a
time Δt ∼ ℏ/(Mc2). Physicists call this a “virtual
particle.”.
Particle in Impenetrable Box!
Note that En =
n2E1.
Suppose now we have an
impenetrable-walled cube with a particle inside it. Now we can
have standing waves of probability in three different
directions, resulting in three different quantum numbers, nx,
ny and nz so that n2
in the equation above, for a particle on a line, is replaced by
nx2 + ny2 + nz2.
THE FAMOUS DOUBLE SLIT!
If two processes can occur in a given experiment, and they are
distinguishable, the probabilities add separately, P12
= |ψ1|2 + |ψ2|2,
but if the processes are indistinguishable, the probability
amplitudes interfere! P12 =
|ψ1 + ψ2|2.
PROBABILITY WAVE
INTERFERENCE
Indistinguishable
probability amplitudes interfere... this is for example what
causes the zeros in the state function of the particle in a
one-dimensional box. The state with −p cannot be
physically distinguished from the state with +p, so the
two probability waves interfere to give standing waves of
probability with zeros, just as the two transverse waves on a
string fixed at both ends can interfere to give standing
waves.
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