Recent content by benedwards2020

Many thanx... Sometimes these maths books can be a bit vague

Homework Statement I have a shape about the origin. It has rotational symmetry but not reflectional symmetry (its an odd star shape!). I have to write down in standard notation the elements of the symmetry group and I have to construct a caley table under composition of symmetries. I...

Well, I'm assuming that its the principles of statistical mechanics that they're after. As I said, I only know of two 'principles'. I am working on quantum theory though and don't know of any separate principles from Boltzmann for this.

Write down the 3 principles underpinning Boltzmanns law and indicate which of these is incompatible with the quantum theory of gases The Attempt at a Solution Well I know two... 1. The conservation of energy 2. Equal probabilities of allowed configurations But I'm a bit stuck...

I have been asked to find whether or not indistinguishability may or may not be ignored from a given sample of atoms at a given temperature. The calculation I have done fine, but my question is given that the criterion for neglecting indistinguishability has to satisfy de broglie...

Ok, that would be \frac{1}{57}+\frac{4}{57}+\frac{16}{57}+\frac{36}{57} which = 1

Ah... So for P(2h) this corresponds to psi(+2) which has coefficient of -6/sqrt(57) yes? which gives us by modulus square of coefficients 36/57?

Oh dear... Back to the books again I think... My paper asks for probabilities for each of the measurements and gives an example similar to the answers I just gave... I can honestly say that quantum stuff really isn't my forte! What should I be looking out for when calculating probabilities?

So the probability for each of the measurements S: -h, 0, 2h will be simply P(-h) = -1/(sqrt(57)) P(0) = 0 P(2h) = 4/(sqrt(57)) Is this right?

Sorry... Of course \frac{1}{N} \times \frac{36}{N} = \frac{36}{N^2} So \frac{57}{N^2} has N = 7.5498

Ah.. I see what you mean.. \frac{1}{N} \times \frac{36}{N} = \frac{1}{N^2} Therefore I should have \frac{1}{N^2}+\frac{4}{N^2}+\frac{16}{N^2}+\frac{36}{N^2} = 1

\frac{2 \times 5}{3 \times 7}=\frac{10}{21} Am I right in saying that \frac{1}{N}\left(\frac{1}{N}+\frac{4}{N}+\frac{16} {N}+\frac{36}{N}\right) = 1 but wrong in how I've multiplied it out?

I just multiplied out the brackets as you would normally... Something tells me I'm wrong here...

Hmm... I'm probably missing some vital piece of knowledge here... My books aren't very explicit in describing this situation... In fact I am finding the whole quantum physics stuff a bit hard to follow... But anyhow For the points you raise... (i) I understand your point about the squared...

Homework Statement A quantum system has a measurable property represented by the observable S with possible eigenvalues nh, where n = -2, -1, 0, 1, 2. The corresponding eigenstates have normalized wavefunctions \psi_{n}. The system is prepared in the normalized superposition state given by...