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  1. C

    Hamiltonian for elastic collision

    Intuitively, I aggree with dipole's opinion. Since you want to describe an elastic collision, adjust the parameters of the sharp function that you chosed, so that the Hamiltonian and the momentum have vanishing Poisson brackets.
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    Continuity in Minkowski space

    I took the wikipedia's definition of Minkowski space: a 4-D real vector space with a symmetric, bilinear, non-degenerate quadratic form with signature (1,3). From this point of view, can a consistent metric induced by that quadratic form? If not, then according to your comment, I will have to...
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    Continuity in Minkowski space

    How "continuity" of a map Τ:M→M, where M is a Minkowski space, can be defined? Obviously I cannot use the "metric" induced by the minkowskian product: x\cdoty = -x^{0}y^{0}+x^{i}y^{i} for the definition of coninuity; it is a misinformer about the proximity of points. Should I use the Euclidean...
  4. C

    On the axioms of vector space

    So, that would be true if the function: 1\cdot : V→V , 1\cdot:X→1\cdotX is surjective? But this is an extra axiom, more complicated than it's substitute (that is (2)). Better keep (2) as it is... :smile: Thank's for your replies!
  5. C

    On the axioms of vector space

    Hello, I'd like to make a, probably stupid, question regarding the axioms that define a vetor space. Among them, there are the axioms: λ\cdot(μ\cdotX) = (λμ)\cdotΧ (1) and 1\cdotΧ=Χ (2) for all λ,μ in the field and for all X in the vector space, where 1 is the identity of the...
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    Potential formulation of Electrodynamics with magnetic sources

    Would you mind if I decribe you my attempt to find some potentials? As it looks so far, I have managed to find some potentials that represent the fields (where the connection between fields and the potentials is more compicated then the usual one) and also I managed to find the gauge...
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    Eigenvalue for 1D Quantum Harmonic Oscillator

    What means that a function is an eigen-function of some operator? Doesn't this mean that when you act with that operator on that function, the result will be the original function multiplied by a constant (where this constant is the eigenvalue)? So, try to operate with HQHO on u(q) and see what...
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    Potential formulation of Electrodynamics with magnetic sources

    @Vanhess71 I understand that in order to explain the charge quantization, one has to assume the existence of magnetic monopoles. But my concern is not why should there be some magnetic charge. What I want to do is to axiomaticaly accept the existence of magnetic sources (i.e. the existence of a...
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    A Maxwell's equation in differential forms formalism

    Homework Statement This is not actually a homework but a personal work. Here it is: Using the differential forms: F=\tfrac{1}{2!}{{F}_{\mu \nu }}d{{x}^{\mu }}\wedge d{{x}^{\nu }} and J=\tfrac{1}{3!}{{J}^{\mu }}{{\varepsilon }_{\mu \alpha \beta \gamma }}d{{x}^{\alpha }}\wedge d{{x}^{\beta...
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    Gravity and magnetism

    In Newtonian theory it affects EVERYTHING which has the property of "mass". In GR theory it affects EVERYTHING, since it apperars in the equations of motion (geodesic equations). So, yes, according to us so far understanding of gravity, gravity affects everything, reagrdless its space scale.
  11. C

    Write Vector Expression in n-t and x-y coordinates of Acceleration

    Why don't you try to express en and et in terms of ex and ey ? Doing that, you can find the total acceleration, a = an + an , in terms of its projections on x and y axis. * e i is the unit vector in the direction of the subscript "i".
  12. C

    Potential formulation of Electrodynamics with magnetic sources

    Sorry, but I can't acces to the papers at the links. Can I find them somewhere else, for free? And something else: as I deduced from the titles, these papers seemed to refer to the subject at quantum level. If correct, is there somehting in classical level?
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    Generalization of force.

    I think that if there was such a force, then the definition of "force", i.e. F = \dot{p} woulld be inconsistent, since the magnitude that defines the force (\dot{p}) would be in what we want to define (F) . To me, it looks non-sence to define "something" using terms that invlolve that "something".
  14. C

    Potential formulation of Electrodynamics with magnetic sources

    Hello! I am trying to construct (if it is possible) a potential formulation of an electromagnetic theory which permits the presence of magnetic sources, using as a starting point the equations referred here: Although I think that I have make some...
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    Question on the derivation of Intensity

    "u" is energy density, right? So, for a given volume ΔV you can find the energy content of it, using the relation ΔE = u ΔV. Ok, so far? If yes, then consider a given surface ΔA and try to find the energy passed through it for some time interval Δt. That amount of energy, after leaving the...
  16. C

    Charged Sphere with a Hole - Check my work?

    This holds if the disk's center is at the origin, at z=0. But this disk is at z = a , so in your equation make the substitution z → z-a . I think that the rest are correct...
  17. C

    Determing the composition of a state

    P(ω1) = |<ω1|v>|2 , so: a = 1/2 and b will be (3/4)1/2 multiplied by an arbitary phase factor.
  18. C

    Eigenvalues of Hamiltonian

    I made a mistake... This is the system: \begin{align} & {{\Omega }_{0}}{{c}_{i2}}={{\omega }_{i}}{{c}_{i0}} \\ & {{\Omega }_{1}}{{c}_{i2}}={{\omega }_{i}}{{c}_{i1}} \\ & {{\Omega }_{0}}{{c}_{i0}}+{{\Omega }_{1}}{{c}_{i1}}={{\omega }_{i}}{{c}_{i2}} \\ \end{align} Now, setting...
  19. C

    Eigenvalues of Hamiltonian

    Start with this: Consider this linear combination: \left| {{\psi }_{i}} \right\rangle ={{c}_{i0}}\left| 0 \right\rangle +{{c}_{i1}}\left| 1 \right\rangle +{{c}_{i2}}\left| 2 \right\rangle These superpositions will be eigenstates if: {{H}_{I}}\left| {{\psi }_{i}} \right\rangle...
  20. C

    Eigenvalues of Hamiltonian

    I just added this...
  21. C

    Eigenvalues of Hamiltonian

    Since the hamiltonian consists of the states |0> , |1> and |2> , these will be a basis for it's non-zero eigenvalue eigenstates, because, if you acted with the hamiltonian to every other state |n>, you will get zero (assuming that |n>'s are a complete set of orthonormal states). So, try to act...
  22. C

    Partial derivative chain rule for gradient

    You don’t sum... Gradient is a vector and what you have found are the linearly independent components of it.
  23. C

    Electromagnetism its counterpart particle? And can it be used to create a PMF?

    OK, first a correction. EMF is not created only by electrons, but by every kind of particle that has the fundamental property of "electric charge". There are many kinds of such elementary particles: electron, muon, tau, quarks, W bosons and their antiparticles (what you call "negative...
  24. C

    Reversal of limits of integration in the derivation of probability current density

    Let me give you an alternative way to derive the current's expression, which maybe has more sense. What we are looking for is a function that satisfies the “continuity equation”: {{\partial }_{t}}\rho +{{\partial }_{x}}j=0 which comes from the requirement of local conservation of probability...
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    Spin in elementary particles

    "What is spin?" is a question of the species "What mass, charge, or color is?" and the answer is the same: "A fundamental property of elementary particles". I think that this property had been observed for the fist time in the famous "Stern–Gerlach experiment" or, according to wikipedia, "in the...
  26. C

    PV Diagram help - Monatomic ideal gas change of state

    Do you really need n to calculate the change in internal energy? Remember that U depends only on temperature, so what is the temperaure difference?
  27. C

    Proof of Gauss's law, starting from Coulomb's Law?

    Coulomb's law for a point charge in the origin is: \mathbf{E}\left( \mathbf{r} \right)=\frac{q}{4\pi {{\varepsilon }_{0}}}\frac{{\mathbf{\hat{r}}}}{{{r}^{2}}} When you integrate the field on an arbitrary closed surface (that includes the origin): \oint\limits_{S}{\mathbf{E}\cdot...
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    Interesting snowball down slope; increasing mass

    oops.:redface: I forgot about it... I'll see if I can do something else
  29. C

    Interesting snowball down slope; increasing mass

    Take a look at this for part b) (which also answers a) ). I combine the equations: dm=adx\Rightarrow \dot{m}=av and \frac{d}{dt}\left( mv \right)=g\sin \varphi to get the separable differential equation: m\dot{v}+a{{v}^{2}}=g\sin \varphi which is solved as: \begin{align}...
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    [QM] Total angular momentum rotation operator

    Almost... To show that a state is an eigenstate of some operator, all you have to do is to show that when that operator acts on that state, gives the same state multiplied by some constant (like the last of the equalities I presented). In general, U|jm> does not have to be equal to |j,-m>, since...
  31. C

    Thought experiment

    It's pretty simple and doesn't need futher arguing: Force = f(v) (function of velocity, where the functional form depends on shape) Power loss = f(v)\cdotv (equall for both ships) To keep velocity or kinetic energy constant, you have to give energy at the same rate of losing it. But...
  32. C

    Thought experiment

    Of course, this is an exactly solvable problem and we have the tools to do it. Polls are needed when there is not an objective answer, which of course is not the case of this problem.
  33. C

    Thought experiment

    I agree... The force depends on the velocity and shape, so they are the same, and since the spaceships are co-traveling, they lose energy with the same rate since: Power = f v = rate of energy loss Your brother is partly right, since more mass means less deceleration, but also more mass means...
  34. C

    The work done by an electric field in accelerating a charged particle?

    A) correct! B) correct! C) You are right! D) The change in P.E. will be equall to minus the gain in K.E. (conservation of energy)
  35. C

    [QM] Total angular momentum rotation operator

    You have to use the equation: U\left[ {{R}_{1}}\left( \pi \right) \right]{{J}_{3}}{{U}^{-1}}\left[ {{R}_{1}}\left( \pi \right) \right]=-{{J}_{3}} which comes from the transformation law of the rotation generators: U\left( R \right){{J}^{ij}}{{U}^{-1}}\left( R...
  36. C

    Constant of motion, Maxwell's equations

    It looks ok! Maybe the unused equation was given for sake of completness, letting you decide if it will be used or not.
  37. C

    Simple algebra to find the strict mass–energy equivalence formula, and I cant do it

    OK, I thought you had say to use the formula for E twice, sorry...
  38. C

    Simple algebra to find the strict mass–energy equivalence formula, and I cant do it

    That will not solve anything... The formula for the momentum has to be used. I recommend you to start with "p = γmv" and find "v" as a function of "p", then find "γ" as a function of "p" and finaly replace "γ" in "E=γmc2" with what you have found.
  39. C

    Mass of an accelerated electron?

    Yes Yes, I just referred the reasoning for doing this...
  40. C

    Mass of an accelerated electron?

    This is OK! The electron gains energy qV , so total energy will be: E = m0c2 +qV = m c2 or m = m0 + qV/c2
  41. C

    1 d motion free fall problem

    Sorry, I have misread the question. You should find the time needed for the shoe to touch the ground, solving the equation h = 1/2 g Δt2 for Δt. Thren subtract it from 3.8s...
  42. C

    Validating the kinetic energy for the two particle collision problem

    I guess it can be done that way, althought I had something else in mind: \frac{dE}{dt}=0\Rightarrow \frac{dT}{dt}+\frac{dV}{dt}=0\Rightarrow \frac{dT}{dt}+\frac{\partial V}{\partial {{x}_{1}}}{{v}_{1}}+\frac{\partial V}{\partial {{x}_{2}}}{{v}_{2}}=0\Rightarrow \Rightarrow...
  43. C

    1 d motion free fall problem

    Revise c) (Δx = 1/2 g Δt2 and include the displacement during deceleration) I found 48.4 m About d), what is the height of the tower? Use the formula v = √(2gh) About e), the fall lasts 2.6s+1.2s = 3.8s. Find shoe's displacement fot that time and subtract it from the height.
  44. C

    Electricity and magnetism confusion!

    The filed at r=ri wil be: E = -dV/dr ≈ -ΔVi/Δri where ΔV = V(ri+1)-V(ri) and Δri = ri+1-ri
  45. C

    Validating the kinetic energy for the two particle collision problem

    When we say tha energy is conserved, we mean that is constant as time passes. So the derivative of energy w.r.t. time will be zero. Althought V depends explicitly on x = x1-x2, since x1 and x2 are functions of time, then V is actually a function of time. So try to differntiate T+V=E w.r.t. time...
  46. C

    Invariance of schroedinger equation

    Try to change the wavefunction as well: multiply it by a space-time dependent phase factor.
  47. C

    Can't understand the algebraic theory of spin.

    No, you don’t call the half-integer eigenstates “spin” and the others “angular momentum eigenstates” (<- the correct term is “orbital angular momentum”, but this is not the problem here). Since all of them are eigenstates of some angular momentum operator (which in algebraic theory of angular...
  48. C

    Can't understand the algebraic theory of spin.

    I understand that this is too much information and maybe it is quite ambiguous to you about how to use it to get results. When you clear these up, if you would like, I could guide you in some examples on how to use them.