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    How do I see if the equations of motion are satisfied?

    Homework Statement (a) Calculate the Conserved currents $$K_{\mu \nu \alpha} $$ associated with the global lorentz transformation and express them in terms of energy momentum tensor. (b) Evaluate the currents for $$L=\frac{1}{2}\phi (\Box +m^2)\phi$$. Check that these currents satisfy...
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    Cylinder parallel to a constant external B field

    Homework Statement A cylinder of permeability ##\mu## is placed in an external field ##B_0##. find the strength and direction of magnetic field inside the cylinder for: a) when axis of cylinder is parallel to external field. b) when axis of cylinder makes an angle ##\theta _0## with external...
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    Finding canonical transformation

    I actually couldn't figure out how to edit the question and insert more details into it so I just created another thread at: "https://www.physicsforums.com/threads/canonical-transformation-two-degrees-of-freedom.846585/#post-5309162" and I included my attempt at solution there (I have actually...
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    Canonical Transformation (two degrees of freedom)

    so using the Hamiltonian equations of motion I have: $$\dot{Q_1}=\frac{\partial H}{\partial P_1}=aP_1 \Longrightarrow \frac{d(q_1^2)}{dt}=2q_1\dot{q_1}=aP_1\\\dot{Q_2}=\frac{\partial H}{\partial P_2}=b \Longrightarrow \dot{q_1}+\dot{q_2}=b\\\dot{P_1}=0\\\dot{P_2}=0$$ So I guess these are the...
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    Canonical Transformation (two degrees of freedom)

    Homework Statement Point transformation in a system with 2 degrees of freedom is: $$Q_1=q_1^2\\Q_2=q_q+q_2$$ a) find the most general $P_1$ and $P_2$ such that overall transformation is canonical b) Show that for some $P_1$ and $P_2$ the hamiltonain...
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    Finding canonical transformation

    Homework Statement If in a system with i degrees of freedom the $$Q_i$$ are given what is the best way to proceed for finding the $$P_i$$ so that we have an overall canonical transformation. say for a two degree freedom system we have $$Q_1=q_1^2 $$ and $$ Q_2=q_1+q_2$$ Homework Equations...
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    Collision of two photons using four-momentum

    Thank you so much I have found it. it will be as following: the four momentum of system after the collision and creation of two identical particle will be: $$p^{\mu}_T=(2 \gamma mc,0,0,0)$$ now using $$\gamma=1$$ and using the invariance of the square of the total momentum in a reaction we get...
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    Collision of two photons using four-momentum

    Then how do we do we solve the last part (part d), I thought i was gonna need it for determining the minimum energy.
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    Collision of two photons using four-momentum

    Can we use the Lorentz boost ti find it? I mean looking for a transformation that makes the spatial components of the total four momentum vanish?
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    Collision of two photons using four-momentum

    Homework Statement Two photon of energy ##E_1 ## and ## E_2## collide with their trajectory at an angle $\theta$ with respect to each other. a) Total four-momentum before collision? b) square length of 4-momentum in lab frame (LB)and in center of momentum frame (CM)? c) 4-momentum of two photon...
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    Separation of variables and potential

    Homework Statement A potential satisfies ##\nabla^2 Φ = 0## in the 2d slab ## -\inf < x < \inf ##, ##-b < y < b ##, with boundary conditions ## Φ(x, +b) = +V_s(x)## on the top and ##Φ(x, b) = -V_s(x)## on the bottom, where[/B] ##V_s (x)= -V_0 for -a<x<0## ##V_s (x)=+V_0 for 0<x<a## (a) what...
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    Finding potential using Greens function

    I have actually found out a way to do it, its not through bessels functions though. but thank you for the help
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    Quantum mechanics operators

    should I solve it without the resolution of Identity?
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    Quantum mechanics operators

    since the problems says for every state A so should I write as following ##<A_i|L|A_i>=0 \to ## then as before ## <B_j|L|A_i>=\sum_{i}<B_j|A_i><A_i|L|A_i>=0## is it right now?
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    Quantum mechanics operators

    Homework Statement Suppose a linear operator L satisfies <A|L|A> = 0 for every state A. Show that then all matrix elements <B|L|A> = 0, and hence L = 0. Homework Equations ##<A|L|A>=L_{AA} and <B|L|A>=L_{BA}## The Attempt at a Solution It seems very straight forward and I don't know how...
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    Finding potential using Greens function

    Homework Statement A potential ##\phi(\rho, \phi ,z)## satisfies ##\nabla^2 \phi=0## in the volume ##V={z\geqslant a}## with boundary condition ##\partial \phi / \partial n =F_{s}(\rho, \phi)## on the surface ##S={z=0}##. a) write the Neumann Green's function ##G_N (x,x')## within V in...
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    Relativistic Quantum Mechanics

    @naturale and by the way naturale can you please show me the steps how you get that? we put the solution into ψ=Z(z)T(t) get the follwoing: ψ(z,t)=(Ae^{iωt} + Be^{-iωt})(Ce^{ikz} + De^{-ikz}) how do we apply the periodic conditions to this??
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    Relativistic Quantum Mechanics

    @Fredrik well Im sorry I'm not really that good with -Latex- since i have just started using it. for the momentum Im just applying the following formula: π_μ = \frac{∂L}{∂(∂_μψ)} and applying this to lagrangian L=(1/2)[(∂ψ/∂t)^2 -(∂ψ/∂z)^2 -m^2ψ^2] we get the follwing : π_0 =...
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    Relativistic Quantum Mechanics

    @Fredrik what I mean is that we have two partial derivatives (with respect to t,z) present in the Lagrangian so we have to apply the following formula: \frac{\partial L}{\partial ψ} = \sum_{i=1}^\infty \frac{\partial (\frac{\partial L}{\partial ψ_xi})}{\partial x_i} where x_i...
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    Relativistic Quantum Mechanics

    the problem is on page 26 of "relativistic quantum mechanics and field theory" by Franz Gross. consider the lagrangian density: L=(1/2)[(∂ψ/∂t)^2 -(∂ψ/∂z)^2 -m^2ψ^2] a) find the momentum conjugate. b) find the equation of motion for the fields and the solution. use periodic boundary...
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