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# Zeeman effect solved

By Tejman’s United Nature-Wave theory.

Tejman Chaim Henry. Jerusalem.

United Nature Theory-Wave Theory

Zeeman effect belong to the most important scientific works

Zeeman effect = the virtual behavior of most connections in the NATURE.

Zeeman effect named after the Dutch physicist Pieter Zeeman, is the effect of splitting a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field. Also similarly to the Stark effect, transitions between different components have, in general, different intensities, with some being entirely forbidden (in the dipole approximation), as governed by the selection rules.

Since the distance between the Zeeman sub-levels is a function of the magnetic field, this effect can be used to measure the magnetic field, e.g. that of the Sun and other stars or in laboratory plasmas. The Zeeman effect is very important in applications such as nuclear magnetic resonance spectroscopy, electron spin resonance spectroscopy, magnetic resonance imaging (MRI) and Mössbauer spectroscopy. It may also be utilized to improve accuracy in atomic absorption spectroscopy. A theory about the magnetic sense of birds assumes that a protein in the retina is changed due to the Zeeman effect.[1] When the spectral lines are absorption lines, the effect is called inverse Zeeman effect.

In the presence of an external magnetic field, the weak-field Zeeman effect splits the 1S1/2 and 2P1/2 states into 2 levels each () and the 2P3/2 state into 4 levels (). The Landé g-factors for the three levels are:for (j=1/2, l=0)   for (j=1/2, l=1) for (j=3/2, l=1). Note in particular that the size of the energy splitting is different for the different orbitals, because the gJ values are different. On the left, fine structure splitting is depicted. This splitting occurs even in the absence of a magnetic field, as it is due to spin-orbit coupling. Depicted on the right is the additional Zeeman splitting, which occurs in the presence of magnetic fields.

## Theoretical presentation

The total Hamiltonian of an atom in a magnetic field iswhere is the unperturbed Hamiltonian of the atom, and is perturbation due to the magnetic field:where is the magnetic moment of the atom. The magnetic moment consists of the electronic and nuclear parts; however, the latter is many orders of magnitude smaller and will be neglected here. Therefore,where is the Bohr magneton, is the total electronic angular momentum, and is the Landé g-factor. The operator of the magnetic moment of an electron is a sum of the contributions of the orbital angular momentum and the spin angular momentum , with each multiplied by the appropriate gyromagnetic ratio: where and (the latter is called the anomalous gyromagnetic ratio; the deviation of the value from 2 is due to Quantum Electrodynamics effects). In the case of the LS coupling, one can sum over all electrons in the atom:where and are the total orbital momentum and spin of the atom, and averaging is done over a state with a given value of the total angular momentum.                                           If the interaction term is small (less than the fine structure), it can be treated as a perturbation; this is the Zeeman effect proper. In the Paschen-Back effect, described below, exceeds the LS coupling significantly (but is still small compared to ). In ultrastrong magnetic fields, the magnetic-field interaction may exceed , in which case the atom can no longer exist in its normal meaning, and one talks about

 Zeeman effect on a sunspot spectral line Solar magnetogram

Breit-Rabi solution formula we will include the hyperfine structure (interaction between the electron's spin and the magnetic moment of the nucleus), which is governed by the quantum number , where is the spin angular momentum operator of the nucleus. Alternatively, the derivation could be done with only. The constant is known as the zero field hyperfine constant and is given in units of Hertz. is the Bohr magneton. and are the electron and nuclear angular momentum operators. and can be found via a classical vector coupling model or a more detailed quantum mechanical calculation to be:                                      As discussed, in the case of weak magnetic fields, the Zeeman interaction can be treated as a perturbation to the basis. In the high field regime, the magnetic field becomes so large that the Zeeman effect will dominate, and we must use a more complete basis of or just since and will be constant within a given level.

To get the complete picture, including intermediate field strengths, we must consider eigenstates which are superpositions of the and basis states. For , the Hamiltonian can be solved analytically, resulting in the Breit-Rabi formula. Notably, the electric quadrapole interaction is zero for (), so this formula is fairly accurate.

To solve this system, we note that at all times, the total angular momentum projection will be conserved. Furthermore, since between states will change between only . Therefore, we can define a good basis as:We now utilize quantum mechanical ladder operators, which are defined for a general angular momentum operator asThese ladder operators have the propertyas long as lies in the range (otherwise, they return zero). Using ladder operators and We can rewrite the Hamiltonian as                       Now we can determine the matrix elements of the Hamiltonian:Solving for the eigenvalues of this matrix, (as can be done by hand, or more easily, with a computer algebra system) we rrive at the energy shifts:

where is the splitting (in units of Hz) between two hyperfine sublevels in the absence of magnetic field ,

is referred to as the 'field strength parameter' (Note: for the square root is an exact square, and should be interpreted as ). This equation is known as the Breit-Rabi formula and is useful for systems with one valence electron in an () level.[3][4]

Note that index in should be considered not as total angular momentum of the atom but as asymptotic total angular momentum. It is equal to total angular momentum only if otherwise eigenvectors corresponding different eigenvalues of the Hamiltonian are the superpositions of states with different but equal (the only exceptions are ).

# Zeeman Effect in Hydrogen

When an external magnetic field is applied, sharp spectral lines like the n=3→ 2 transition of hydrogen split into multiple closely spaced lines. First observed by Pieter Zeeman, this splitting is attributed to the interaction between the magnetic field and the magnetic dipole moment associated with the orbital angular momentum. In the absence of the magnetic field, the hydrogen energies depend only upon the principal quantum number n, and the emissions occur at a single wavelength.

Note that the transitions shown follow the selection rule which does not allow a change of more than one unit in the quantum number

The pattern and amount of splitting are a signature that a magnetic field is present, and of its strength. The splitting is associated with what is called the orbital angular momentum quantum number L of the atomic level. This quantum number can take non-negative integer values. The number of split levels in the magnetic field is 2 * L + 1. The following figure illustrates the Zeeman effect.

 The Zeeman Effect

Atomic physicists use the abbreviation "s" for a level with L=0, "p" for L=1, and "d" for L=2, and so on (the reasons for these designations are of historical interest only). It is also common to precede this designation with the integer principle quantum number n. Thus, the designation "2p" means a level that has n=2 and L=1. In the preceding example the lowest level is an "s" level, so it has L=0 and 2L + 1 = 1, so it isn't split in the magnetic field, while the first excited state has L=1 ("p" level), so it is split into 2L + 1 = 3 levels by the magnetic field. Thus, a single transition is split into 3 transitions by the magnetic field in this example. The Zeeman effect can be interpreted in terms of the precession of the orbital angular momentum vector in the magnetic field, similar to the precession of the axis of a spinning top in a gravitational field.http://csep10.phys.utk.edu/astr162/lect/light/zeeman-split.html

For better understanding Zeeman effect  cxxsee Electron motion, spin, waltz solution-Tejman.

This swirling rotation and revolving motion of electric strong force path create two semi loops quantum formations.

 Black hole or energetic source expell.energetic pathr moving by curvatures and by dint of its swirling and spinning space time behaviors create open continue quanta formations and. exactly like known retrograde motion. Wave formation: (quantum).The energetic loop to the right (of both pictures) pushes outward, while the magnetic-gravity loop (left) pushes the energetic matter inside.

Every stable {quantum} formation must have two behaviors: Electric {strong force} semi-loop and gravity-magnetic {weak force} of 6 quarks [+ +and -] and gravity semi loop [- - and+] which must be in equilibrium in all phase transitions. See Tejman phase transitions

For understanding quantum endless formations please see some examples

Different quanta formations

Example: Two semi loops- by strong force- closed quanta formations

Picture, GALAXY M-51 closed quantum formation.

 Stefan's Quintet. 7317- merging galaxy[quantum] NASA M-51 The magnetic swirl, to the right, and the energetic swirl, left- together quantum- gravitational wave formation. Independent closed quantum formation connected by energe- tic paths They are not collisions galaxies

Two semi loops of the one quantum formation connected by path.

 Electric part of M-51 + lt Gravity magnetic part M-51-rt

Other connections

Two Semi loops open quanta formations by continue energetic path.

 Motion of energetic matter From Hubbell Telescope. Motion of energetic matter in DNA

Other type  of quanta closed gravity semi loop quantum.

Gravity super nova, earth, sun, electron [two electrons virtual molecule], neutrino living creation,. molecules. electron galaxies, universes they are

stabile formations that means that they are quanta two forces and Tejman’s article “Electron motion spin explained the NATURE ingenious creation.

in closed gravity semi loop electron on basis NATURE observations and conclusion.

 2 3 4

1 Aurora earth prominence. Gravity semi loops quantum

2 From electric swirl continue energetic path which by swirling motion create second swirl [like white hole-Schwarzschild swirl]

3 Schwarzschild swirl by retrograde motion create gravity paths

4 Gravity path by peculiar motion move to ‘”south pole” and create

create like ‘black hole” which create again electric path to continue motion of energetic matter in closed gravity semi loop and bubble [electron\.

Coriolis forces are forces of closed quantum formation

(1)(2)(3) The motion of Coriolis force (Energetic matter motion)        (4)(5)(6) Coriolis Force – the force is the same however it has two different representations at the northern and southern parts of the earth, hence the different

Gravity path from North Pole [-] to South Pole and electric paths [+] from South Pole to North direction.

Pict. From Neutron stars by Steve Nadis [astronomy march 1999] p.52.

## Expelled energetic path from energetic creation create quanta formations,

Circulation  of energetic matter in electron, bubble and closed quantum formation.

 1

1      Electric swirl  [Kerr, black hole]

2      Expelled electric path [with clockwise rotation Coriolis forces]

3      Creates white hole swirl [Schwarzschild swirl]

 4 5 6

4      Schwarzschild swirl creates magnetic path [Coriolis contra clockwise forces]

5      Those forces move from north to south

6      Create closed energetic circulation in electron [closed gravity quantum formation]

That means electron, earth are closed quanta formations.

Virtual quanta not connected by energetic path only by virtual wave forces.

The quanta behavior is endless so appears different quanta formations and equations [but always with balance of both forces semi ].

 Schrödinger’s equation: Faraday’s equation: Maxwell equation: Planck’s equation: Einstein’s  equation:

The de Broglie equation   f =E/h,  or  E= fXh

Tejman’s equation claims: that for stabile quantum formation must always be energetic equilibrium of [two semi loops] bubbles forces.

This mixed electromagnetic force [two semi loops bubbles] appears in superposition [of two bubbles behaviors] as one entity like Schrödinger’s cat paradox.

The ideal structure of energetic matter is the wave formation, which is comprised of an energetic and magnetic loop. Under ideal conditions, such as the photon, the two loops are equal insofar as the properties of their energetic matter are concerned.

The structure of the wave formation is amenable to the creation of various life forms. Any change in the proportion of energetic matter in the loops leads to a new phase transition in which one of the loops has more energetic properties. These changes to the equilibrium between the energetic and magnetic loop result in different behaviors.

To follow are mathematical equations for the balance between the energetic and magnetic loop of a wave formation in various phase transitions:

1. High Energetic Phase Transition (Hyperspace):

 Energetic Loop(x) = Magnetic Loop = 1 = 1 Energetic Loop(x) Magnetic Loop Energetic Loop(x) Magnetic Loop

In hyperspace, energetic matter (energy, space and time) propagates endlessly, while the magnetic loop (matter) almost disappears.

2. The Duality Phase:

 Energetic Loop = Magnetic Loop = 1 = 1 Magnetic Loop Energetic Loop

The phase transition of a photon is in a state of duality whereby the magnetic loop equals the energetic loop, which equals 1. In this phase, both loops are balanced and therefore the photon has the longest lifespan.

3. Low Energetic-High Magnetic Phase Transition

 Magnetic Loop(x) = Energetic Loop = 1 = 1 Energetic Loop(x) Energetic Loop Magnetic Loop(x) Magnetic Loop
 In this phase, the magnetic loop is induced to compliment the energetic loop by accelerating the pace at which it spins. This helps maintain the equilibrium of the wave. Moreover, energy, space, and time are most condensed in this phase, as the magnetic properties (loop) gain the ascendancy! In fact, this is exactly what transpires in a nuclear bomb, as extremely condensed units of energy, space and time are released by the explosion. Every quantum formation transferee from high energetic level [phase] to lower energetic level by dispersing energetic matter. Two like electrons, atoms or molecules create virtual quantum [not connected by strong foces. The one electron became electric properties and second gravity spin like atoms molecules and isomers formations and easy separate [Quantum formation by energetic path very difficult to split]      . Electron - Virtual weak connection Electron + Quarks d d u Quarks u u d

Very simple explanation of quantum structure and behavior of virtual quantum of 2 electrons not connected by strong force only by virtual energetic path   This virtual connection is the most ingenious sophisticated of NATURE creation of endless different creations mainly of living formation.

This picture explained electrons e+ and electron e- behavior and Zeeman effect 1 2 3. and 1 2 3 quarks lines

 csep10.phys.utk.ed The Zeeman Effect en.wikipedia.org Zeeman effect - Wikipedia en.wikipedia.org inverse Zeeman effect. faculty.gvsu.edu as the Zeeman effect.

In all quanta equations, energetic matter-forces are in superposition,

That means that electron ruled by two forces in gravity phase transition. Electron the most condensed wave formation creates closed wave particle, closed quantum formation [example chicken eggs see gravity semi loop.

All quanta equations are viable also to electron closed quantum in gravity phase transition

Summary

Zeeman effect = the virtual forces behavior are the most connections in NATURE including living creations.

 Yours waves quanta  frequency are very nice, adorable. Yours          waves  quanta frequency are pfu,  , pfu

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