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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

    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

    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

    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

    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

    Homework Statement Find the indefinite integral of \int \frac{sec^2 x}{\sqrt{1-tan^2 x}} dx I'm stuck on how to proceed with the denominator. I know that \sqrt{1+tan^2 x} is equivalent to \\sec\theta but I cant seen to find an equivalent to what I have. Can anyone give me...
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    Volume of the solid of revolution

    Find the volume of the solid of revolution obtained when the region under the graph of f(x) = \left( \frac{1}{x} \right) e^\frac{1}{x} from x = 1 to x = 6 Homework Equations \pi \int (f(x))^2 dx The Attempt at a Solution Ok, the equation I gave above should be that...
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    Integrating Natural Log

    I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign) S (x - 2) Ln(3x) I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used f(x) =...
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    Potential Energy

    This question concerns 2 positively charges masses at a certain distance apart. If I have a value for gravitational potential energy of -3.6e-12 J And a value for electrostatic potential energy of 3.6e-12 J Would I be right in saying that the overall potential energy of the system...
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