# klein gordon equation

6. ### A Coulomb Klein Gordon: Where does e^(-iEt) come from?

Hi everyone, I've been reading about the Klein Gordon equation with the Coulomb Potential. The full solution can be found here: http://wiki.physics.fsu.edu/wiki/index.php/Klein-Gordon_equation#Klein-Gordon_equation_with_Coulomb_potential I'm confused near the beginning of this. I understand...
7. ### I Negative and Positive energy modes of KG equation

If we have the normal KG scalar field expansion: $$\hat{\phi}(x^{\mu}) = \int \frac{d^{3}p}{(2\pi)^{3}\omega(\mathbf{p})} \big( \hat{a}(p)e^{-ip_{\mu}x^{\mu}}+\hat{a}^{\dagger}(p)e^{ip_{\mu}x^{\mu}} \big)$$ With $\omega(\mathbf{p}) = \sqrt{|\mathbf{p}^{2}|+m^{2}}$ Then why do we associate...
8. C

### I Deductions of Formulas for Energy

So, I am a newbie in quantum mechanics, took modern physics last fall for my physics minor. I know that Schrodinger based his equation based on the equation K + V = E, by using non-relativistic kinematic energy (P2/2m + V = E) p becoming the operator p= -iħ∇ for the wave equation eigenfunction...
9. ### I Equivalent Klein-Gordon Lagrangians and equations of motion

Suppose one starts with the standard Klein-Gordon (KG) Lagrangian for a free scalar field: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}$$ Integrating by parts one can obtain an equivalent (i.e. gives the same equations of motion) Lagrangian...
10. ### I Wave equation solution using Fourier Transform

I'm studying Quantum Field Theory and the first example being given in the textbook is the massless Klein Gordon field whose equation is just the wave equation \Box \ \phi = 0. The only problem is that I'm not being able to get the same solution as the book. In the book the author states that...
11. ### I When can the Klein-Gordon Equation be used for a photon?

Consider the double-slit experiment done with photons from a laser. If one was interested only in computing position (vertical) probability amplitudes and did not care about spin/helicity, could the Klein-Gordon Equation (with mass set to zero) be used? Thanks in advance.
12. ### Using Noether's Theorem find a continuity equation for KG

1. Homework Statement Consider the Klein-Gordon equation $(\partial_\mu \partial^{\mu}+m^2)\varphi(x)=0$. Using Noether's theorem, find a continuity equation of the form $\partial_\mu j^{\mu}=0$. 2. Homework Equations $(\partial_\mu \partial^{\mu}+m^2)\varphi(x)=0$ 3. The Attempt at...
13. ### A How to derive general solution to the Klein-Gordon equation

I understand that the ansatz to $$(\Box +m^{2})\phi(\mathbf{x},t)=0$$ (where $\Box\equiv\partial^{\mu}\partial_{\mu}=\eta^{\mu\nu}\partial_{\mu}\partial_{\nu}$) is of the form $\phi(\mathbf{x},t)=e^{(iE_{\mathbf{k}}t-\mathbf{k}\cdot\mathbf{x})}$, where...
14. ### Klein-Gordon Hamiltonian commutator

1. Homework Statement Consider the quantum mechanical Hamiltonian $H$. Using the commutation relations of the fields and conjugate momenta , show that if $F$ is a polynomial of the fields$\Phi$ and $\Pi$ then $[H,F]-i \partial_0 F$ 2. Homework Equations For KG we have...
15. ### Klein-Gordon eqn: why dismiss messages at phase velocity

Hi All, I've heard it said that the superluminal phase velocity of the KG eqn is not a problem for relativistic causality because signals travel at the packet/group velocity, which is the inverse of the phase velocity (c being 1). I'm a bit skeptical of this. We can strip away all the quantum...
16. ### How does one derive the Lagrangian densities used in QFT?

I've been working through a qft book by Sadovskii (while I wait for my Peskin book to come in) and I've used some later chapters of Griffith's Into to Elementary Particles as an introduction to some qft. My issue with both of these is that, where in classical mechanics we have the Lagrangian...