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...
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?
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?
Hmm... I'm probably missing some vital piece of knowledge here.... My books aren't very explicit in describing this situation... In fact Im 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...
Determine the possible outcomes of the measurement Sz for the two electrons
\psi = \frac{1}{2} (\psi_{+}(A)\psi_{-}(B)-\psi_{+}(A)\psi_{-}(B))
The Attempt at a Solution
Now I know how to work out the outcomes for each of the pairs, but what I'm not sure about is how to handle the...
Can someone tell me how the outer shell structure is determined from the electronic structure. I know i can look this up but I'd like to know how it is derived and are there any rules I should follow so i can determine them myself?
Is there a standard way of quoting uncertainties for say counting radioactive decay counts?
I know I can use sqrt(n)
And I know I can use fractional uncertainty 1/(sqrt(n)) too.
Is there a standard way of quoting? Apologies if this is in the wrong section
I want to excite the tube with a range of frequencies, and record the length where resonance occurs
I think I see what you mean about the graph not being a straight line... It needs to be in the right form...
Is there a list of similar results I could take a look at somewhere? I think I...
What I'm trying to do is to find the speed of sound in air. I have the resonance experiment in mind where a frequency is applied to a tube of air and measurements taken of the length of the tube where resonance occurs for that particular frequency.
So what you are saying is that I should...
Can someone tell me how I find the speed of sound in air?
If I plot a graph of frequency against length would I be right in saying that I can find the speed of sound by finding where the two points on the graph intersect and multiplying by 2, so that
v = 2 * Lf
Hmm... I don't think I'm following you for the second substitution.... My books don't give me those examples.
If i say that
\frac{1}{(1-u^2)^\frac{1}{2}} = arcsin
But that u = tan(x)
Surely we can conclude that the answer is
arcsin(tan(x)) ?
Ok, that makes sense... Now I have a list of trig identities and I can see that
arctan(x) = \frac{1}{1+x^2}
Again its that half power thats confusing me....
Unless arcsin(x) is correct. Hmm
arcsin(x) = \frac{1}{\sqrt{1-x^2}}
which is the same as
\frac{1}{(1-u^2)^\frac{1}{2}}...
ok, so this will give me
\frac{sec^2 (x)}{\sqrt{1-u^2}}
where
\frac{du}{dx}=sec^2 dx
And to get rid of the root, will give us
\frac{sec^2 (x)}{(1-u^2)^\frac{1}{2}}
Am I right so far?
I need to find the indefinite integral
\int \frac{sec^2 (x)}{\sqrt{1-tan^2 (x)}}
Now, I'm not sure which method to use here.... I think that the quotient and the square root is confusing me here. I can certainly integrate the numerator - thats not the problem, I'm not sure how to...
Ok, I'm happy with how we got to this point.
So what I have now is the integral of 'something' times sec^2(x) dx
Is this right? And now I need to find what makes up the equivalent of the original integral.... Am I on the right lines here?
I think half the problem I'm having with this...
Ok, is there a quick way of identifying what needs to be substituted. At the moment I'm doing it by trial and error, and obviously in an exam, thats not going to be very economical