The Klein-Gordon equation! Here is the simplest field theory: a scalar field $ \phi(t, x) $ that obeys the equation of motion\[\partial_t^2 \psi - \nabla^2 \psi + m^2 \psi = 0,\]where $ \nabla $ is our usual gradient operator, and $ \partial_t = \frac{\partial}{\partial t} $ is a nice short-hand. Plug the Ansatz\[\psi(t, x) = A(k) e^{-iEt + ik \cdot x}\]into the equation and find $ E(k) $ such that the Ansatz solves the equation! Surprise!

Answered: Image /qna-images/answer/8554ce92-d1db-4d1e-9429-f2f6a88be51d.jpg

Answered: The Klein-Gordon equation! Here is the…

Similar questions

Please solve asap i'm studying for my test tomorrow and i need the answer
A point charge +q is placed at (0, 0, d) above a grounded infinite coducting plane defined by z=0.There are no charges present anywhere else. What is the magnitude of electric field at (0, 0, –d)? [JEST 2012] (a) (87€,d² ) (c) 0 (d) (1676,ď²) (b) 0
Consider the special shape pictured in the diagram below. It is a cylinder, centered on the origin with its axis oriented along z, and it has been partially hollowed to leave two cone-shaped cavities at the top and bottom of the cylinder. The radius of the object is a, its height is 2a, and the solid part of the object (the shaded region that is visible in the rightmost panel of the illustration above, which shows a drawing of the cross-section of the object) has a uniform volume charge density of po. Assume that the object is spinning counter clockwise about its cylinder axis at an angular frequency of w. Which of the following operations is part of the calculation of the magnitude of the current density that is associated with the motion of the rotating object as a function of r (select all that apply)?
$ Q2/Evaluate D.ds side of the divergence theorem for the field D = 2xyax + x'yay C/m² and the rectangular parellelepiped formed by the planes x = 0 and 1, y = 0 and 2, and z = 0 and 4.
Find the electric flux crossing the wire frame ABCD of length , width b and whose center is at a distance OP = d from an infinite line of charge with linear charge density λ. Consider that the plane of frame is perpendicular to the line OP (Fig. ). A d Fig. A D b P 8 C
Calculate the charge density, P, associated with the electric field E (with linear distances expressed in m and coefficients with appropriate units) is: costante in tutto lo spazio; uguale a (3, 4,0)=0; 480 (3xz, 4y +z+1, -x + y) expressed in V/m identicamente nulla;
Figure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using direct integration.
A thin plastic rod of length L has a positive charge Q uniformly distributed along its length. We willcalculate the exact field due to the rod in the next homework set. In this set, we will approximatethe rod as several point sources and develop the Riemann sum as an intermediate step on the wayto writing an integral.For those aiming at a P rating, you may use L = 3.0m , Q = 17 mC, and y = 0.11m to calculate theanswer numerically first and substitute variables for them only as required in the problem statement.For those aiming at an E rating, leave L, Q and y as variables. Substitute numbers only whererequired in the problem statement, and only as a last step
Electrodynamics TUT 1.1
Consider an Ising model of 100 elementary dipoles. Suppose you wish to calculate the partition function for this system, using a computer that can compute one billion terms of the partition function per second. How long must you wait for the answer?
Given the array of Fig. 6.1(a) and (b), find the nulls of the total field when d=1/4 and then with d=\/2 and: (a) B=0 , (b) B=n/2 by using this equation: E. = cos e coskd cos e+ B)] d/2 d/2 to 02 d/2 d/2 (a) Two infinitesimal dipoles (h) Far-field observations Fig. 6-1 Geometry of a two-element array positioned along the z-axis.
6. By evaluating both sides of the equation, verify the divergence theorem using the field Ġ= (x² + y² + ²)(xi+yĵ+zk) and the region bounded by the sphere x² + y² + ² = 25.

SEE MORE QUESTIONS