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Grassmann Variables, Supersymmetry and Supersymmetric ...

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Fermionic Path Integral<br />

SUSY<br />

References<br />

The end<br />

<strong>Supersymmetric</strong> harmonic oscillator<br />

<strong>Supersymmetry</strong><br />

<strong>Supersymmetric</strong> harmonic oscillator<br />

Harmonic bosonic oscillator (2).<br />

After simple calculation Hamiltonian can be presented as:<br />

HB = ωB(NB + 1<br />

2 ) = ωBNB + E0<br />

where E0 = 1<br />

2 �ωB is energy of the ground state (vacuum energy).<br />

Operators b † , b act on a state |nB >, <strong>and</strong> the energy spectrum of<br />

the hamiltonian is:<br />

EB = ωB(nB + 1<br />

2 )<br />

where nB = 0, 1, 2..., <strong>and</strong> nB are the eigenstates of the bosonic<br />

number operator.<br />

Anna Pachol GV,SUSY ans SHO

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