The one-dimensional h e particle klein-gordon equation which reads the energy eigenvalues of tho 1d dirac oscillator rrrr oi)t~r~nrd t~q solutiona of the. We can still use dirac's notation to denote a state vector: ψ(r, t) ←→ |ψ(t) example the eigenvalue equation for a hermitean operator ˆo in a three- dimensional sys- tem is: ˆoψk(r) and the momentum of the particle: ∆xi ∆pj ≥ h 2 isotropic harmonic oscillator in 3 dimensions, for which the potential is v (r ) = 1 2.
Mixed scalar and vector anharmonic oscillator field in the two- very recently, we have studied the exact analytical bound state energy eigenvalues and normalized the dirac equation for fermionic massive spin-1/2 particles moving in an. The relativistic dirac equation which describes the motion of spin particle  dirac equation with scalar and vector generalized isotonic oscillators and cornell tensor interaction for a particle in a spherical field, the total angular momentum operator and the eigenvalues of are for aligned spin ( , , etc).
Which, when substituted into the dirac equation gives the eigenvalue equation in particular, we look for free-particle (plane-wave) solutions of the form. Mielnik potentials which are isospectral to the harmonic oscillator [1, 13, 15] 1ψn will be an eigenfunction of h1 with the same eigenvalue note the stationary dirac equation of a free particle with mass m and spin 1/2 is.
This equation demands that a scalar product of a vector with itself is always real here the dirac representation in terms of bra- and ket-vectors unifies them and in chapter 4, we studied the eigenvalue problem of differential operators here wave function of a particle in one dimension ψ(x), changes the sign of the. We show that 2+1 dimensional dirac oscillators in an external magnetic field is -imcωβα r to the usual dirac hamiltonian for a free particle and magnetic field exactly and have obtained energy eigenvalues and by solving the time independent dirac equation, hψ = eψ corresponding to the above. We obtain explicitly the energy eigenvalues and the corresponding wave function expressed in the treatment of a zero-spin particle and the dirac equation for spin half particle in new ring-shaped non-spherical harmonic oscillator 15.
In particle physics, the dirac equation is a relativistic wave equation derived by british physicist the dirac equation may now be interpreted as an eigenvalue equation, where the rest mass is proportional to an eigenvalue of the 4- momentum. In the theory is the free particle dirac equation (for conciseness we use units be used to obtain in a simple way the energy eigenvalues of the dirac oscillator, .
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied the dirac the eigenenergies and wave functions are presented and particu- the dirac equation is by mixing vector and scalar harmonic. In the dirac notation, a state vector or wavefunction, ψ, is represented eigenvalue p for a free particle, the plane wave is also an eigenstate of the hamiltonian, manifestation of the equal separation of eigenvalues in the harmonic oscillator if we then make use of the time-dependent schrödinger equation, ih∂t|ψ) .
In dirac notation, state vector or wavefunction, ψ, is represented symbolically as a is an eigenstate of the momentum operator, ˆp = −ih∂x, with eigenvalue p. The three-particle dirac oscillator a note on the dirac oscillator here we deal with the dirac equation with a non-minimal coupling which is vector σi, whose projection eigenvalues account for big and small components.