Quantum

Question 1

Postulate one

Answer 1

For any system of particles, there exists a continuous, (normally) continuously differentiable, single-valued, normalisable, complex wavefunction, from which all possible predictions about the physical properties of the system can be obtained.

Question 2

Postulate two

Answer 2

Every dynamical variable may be represented by a Hermitian operator who`s eigen values representing the possible results of carrying out a measurement of that dynamical variable.

Question 3

Postulate three

Answer 3

The operator of position and momentum are x and -ih(bar)d/dx respectively . operators representing other dynamical quantities bare the same functional relationship to these as the corresponding classical quantities do to the position and momentum.

Question 4

Postulate four

Answer 4

where a measurement of a dynamical variable of a system is carried out the probability of it being equal to a particular eigen value is proportional to the square of the amplitude of the wavefunction- equal if normalised.

Question 5

The four properties of a wave functions

Answer 5

single valued
Normalisable
continuous
derivative

Question 6

single valued

Answer 6

the particle can not have two probability’s for the same position. The wavefunction can also not have two probabilities values for the same position

Question 7

normalisable

Answer 7

particles must be found in the system

Question 8

continuous

Answer 8

if the wavefunction is not continuous, the gradient of the wavefnction at that point will be undefined. as with any wave, the energy and momentum stored in the wave is related to the curvature and slop of the wave. These must be well-defined.

Question 9

derivative

Answer 9

except where the potential has an infinite discontinuity

Question 10

solutions inside a 1D well

Answer 10

wavefunction(x) =
Acos(kx) + Bsin(kx)

k^2 = 2mE/hbar