What are the difficulties with Klein-Gordon equation?
Relying on the variational principle, it is proved that new contradictions emerge from an analysis of the Lagrangian density of the Klein-Gordon field: normalization problems arise and interaction with external electromagnetic fields cannot take place.
What is the Klein-Gordon equation used for?
The Klein-Gordon equation [208,209] is a relativistic version of the Schrödinger equation that describes the behavior of spinless particles. The equation has a large range of applications in contemporary physics, including particle physics, astrophysics, cosmology, classical mechanics, etc.
Is Klein-Gordon equation linear?
The Klein-Gordon equation is the linear partial differential equation which is the equation of motion of a free scalar field of possibly non-vanishing mass m on some (possibly curved) spacetime (Lorentzian manifold): it is the relativistic wave equation with inhomogeneity the mass m2.
Why do we need relativistic quantum mechanics?
In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles.
Why is Schrodinger’s equation not relativistic?
Why is the Schrodinger wave equation not for relativistic particles? Because it is based on Newtonian physics rather than relativistic. It’s just classic kinetic energy + potential. There is no mass energy, no relativistic corrections etc.
Is relativity part of quantum mechanics?
Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity.
Is Schrödinger equation relativistic?
The Schrödinger equation is a non-relativistic approximation to the Klein-Gordon equation. The properties (momentum, energy.) described by solutions of Schrödinger equation should depend in the proper way of the Galilei reference frame.
Why Schrödinger equation is not valid for relativistic particles?
Is there a Lagrangian for the Klein-Gordon equation?
We \frst ask if there is a Lagrangian for the \feld ˚(x) from which we can derive the Klein-Gordon equation by the principle of least action. We can actually solve this classically. First, we assume there exists a Lagrangian density Lde\fned as L= Z d3xL (1) 1
Do Klein Gordon equations of motion look different in different metrics?
The resulting Klein Gordon equation should not depend on what convention you use for the metric, as you can just multiply by a minus sign to get the relative minus signs correct. The above, however, may give you the impression that equations of motion will not “look” different in different metrics. But that would be wrong.
What is the complex conjugate of the Klein Gordon Field?
where ψ is the Klein–Gordon field, and m is its mass. The complex conjugate of ψ is written ψ. If the scalar field is taken to be real-valued, then ψ = ψ, and it is customary to introduce a factor of 1/2 for both terms.
Is it possible to develop a Lagrangian or Hamiltonian description of scalar variables?
For the \frst, we can develop a Lagrangian description, and for the second, a Hamiltonian description lends itself quite well to quantization. We will assume we have a \feld variable ˚(x) = ˚(x;t) which is real and behaves as a scalar under Lorentz transformation, and drops o to 0 at spatial in\fnity (as well as its derivatives).