Some Strange Implications of Quantum Mechanics
Quantum m,echanics can have some very strange implications.
A particle may be in several places at one. This is a consequence of the state of the particle being described by a wavefunction, with the probability of a particle being in a region of space being described by
The wavefunction is spread out over a region of space, and if the wavefunction is non zero at two different points, then the particle can in a very real sense be at two different points.
A particle cannot have zero energy. Every particle has a minimum non zero energy, called the zero point energy. If the particle is in an infinite square well, then it cannot sit at rest at the bottom of the well. In an infinite square well, with
for
and
outside this region the allowable wavefunctions are
The smallest possible quantum number is
and ifthe energy of the particle is
If
then 
everywhere and the particle does not exist.
A fluid may flow upwards out of a container, as long as the outside is at a lower level than the inside. This is because the wavefunction spreads out and just like normal matter particles, the wavefunction tends towards states of lower potential energy ie the wavefunction gradually flows down.
Quatum particles may be entangled. If two quantum particles are emmitted from the same point at the same time and move in opposite directions, and we measure the state of one of the partciles, then the state of the other is fixed by our measurement even though it's state has not been measured and it may before this measurement have existed in a superposition of states.
