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  1. B

    Symmetry groups and Caley tables

    Many thanx.... Sometimes these maths books can be a bit vague
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    Symmetry groups and Caley tables

    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...
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    Boltzmanns law

    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.
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    Boltzmanns law

    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...
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    Ignoring Indistinguishability

    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...
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    Normalization Factor

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

    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?
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    Normalization Factor

    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?
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    Normalization Factor

    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?
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    Normalization Factor

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

    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
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    Normalization Factor

    \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?
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    Normalization Factor

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

    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...
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    Normalization Factor

    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...
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    EPR argument - possible outcomes

    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...
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    Electronic structure - Outer shell

    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?
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    Uncertainty question

    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
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    Speed of sound in air graph

    Ok... But isn't that formula the same as I suggested in my original post? (assuming the 1st harmonic?)
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    Speed of sound in air graph

    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...
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    Speed of sound in air graph

    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...
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    Speed of sound in air graph

    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
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    Integration problem

    Thankyou.... And many thanks for you help.
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    Integration problem

    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)) ?
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    Integration problem

    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}}...
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    Integration problem

    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?
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    Integration problem

    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...
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    Indefinite Quotients

    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...
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    Indefinite Quotients

    Just had a look at wikipedia. It shows that the more common answer for the derivative of tan(x) is sec^2 (x) or \frac{1}{cos^2 (x)}
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    Indefinite Quotients

    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
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