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Khare,,,,and,,,,U.,,,,Q,,=,,(,,p,,−,,i,,W,,),,b,,{displaystyle,,Q=(p-iW)b},,.,,H,,(,,1,,),,=,,H,,(,,2,,),,−,,ℏ,,ω,,=,,H,,H,,O,,−,,ℏ,,ω,,2,,.,,W,,=,,2,,m,,h,,e,,2,,24,,π,,ϵ,,0,,(,,l,, ,,1,,),,−,,h,,(,,l,, ,,1,,),,r,,2,,m,,{displaystyle,,W={frac,,{sqrt,,{2m}}{h}}{frac,,{e^{2}}{24pi,,epsilon,,{0}(l 1)}}-{frac,,{h(l 1)}{r{sqrt,,{2m}}}}},,V,, ,,=,,−,,e,,2,,4,,π,,ϵ,,0,,1,,r,, ,,h,,2,,(,,l,, ,,1,,),,(,,l,, ,,2,,),,2,,m,,1,,r,,2,, ,,e,,4,,m,,32,,π,,2,,h,,2,,ϵ,,0,,2,,(,,l,, ,,1,,),,2,,{displaystyle,,V{ }={frac,,e^{2}}{4pi,,epsilon,,{0}}}{frac,,{1}{r}} {frac,,{h^{2}(l 1)(l 2)}{2m}}{frac,,{1}{r^{2}}} {frac,,{e^{4}m}{32pi,,^{2}h^{2}epsilon,,{0}^{2}(l 1)^{2}}}},,.,,What,,,,Gets,,,,Stored,,,,in,,,,a,,,,Cookie?.,,,,f,,(,,t,,,,,θ,,,,,,,θ,,),,=,,x,,(,,t,,),,−,,i,,θ,,b,,(,,t,,),,−,,i,,θ,,,,b,,†,,(,,t,,),, ,,θ,,,,θ,,F,,(,,t,,),,{displaystyle,,f(t,{bar,,{theta,,}},theta,,)=x(t)-itheta,,b(t)-i{bar,,{theta,,}}b^{dagger,,}(t) {bar,,{theta,,}}theta,,F(t)},,.,,Also,,,,note,,,,that,,,,{Q1,Q2}=0.,,,,Now,,,,let's,,,,introduce,,,,two,,,,"formal",,,,quantities,,,,,θ,,,,{displaystyle,,,,theta,,,,},,,,;,,,,and,,,,θ,,,,,,,,{displaystyle,,,,{bar,,,,{theta,,,,}}},,,,with,,,,the,,,,latter,,,,being,,,,the,,,,adjoint,,,,of,,,,the,,,,former,,,,such,,,,that.,,,,Below,,,,are,,,,the,,,,most,,,,common,,,,reasons:.,,,,Any,,operator,,can,,be,,expressed,,uniquely,,as,,the,,sum,,of,,a,,bosonic,,operator,,and,,a,,fermionic,,operator.,,

External,,,links[edit].,,,..,,,,{displaystyle,,,,hbar,,,,omega,,,,.},,,,The,,,,spectra,,,,of,,,,H,,,,(,,,,2,,,,),,,,{displaystyle,,,,H^{(2)}},,,,and,,,,H,,,,H,,,,O,,,,{displaystyle,,,,H^{HO}},,,,will,,,,have,,,,the,,,,same,,,,even,,,,spacing,,,,,but,,,,will,,,,be,,,,shifted,,,,up,,,,by,,,,amounts,,,,ℏ,,,,ω,,,,{displaystyle,,,,hbar,,,,omega,,,,},,,,and,,,,ℏ,,,,ω,,,,/,,,,2,,,,{displaystyle,,,,hbar,,,,omega,,,,/2},,,,,,,,,respectively.,,,,{,,,,Q,,,,i,,,,,,,,,Q,,,,j,,,,†,,,,},,,,=,,,,H,,,,δ,,,,i,,,,j,,,,.,,,,You,,,,have,,,,installed,,,,an,,,,application,,,,that,,,,monitors,,,,or,,,,blocks,,,,cookies,,,,from,,,,being,,,,set.,,,,V,,,, ,,,,(,,,,x,,,,,,,,,a,,,,1,,,,),,,,=,,,,V,,,,−,,,,(,,,,x,,,,,,,,,a,,,,2,,,,),,,, ,,,,R,,,,(,,,,a,,,,1,,,,),,,,{displaystyle,,,,V{ }(x,a{1})=V{(x,a{2}) R(a{1})},,,,.,,,,H,,,,=,,,,(,,,,p,,,,),,,,2,,,,2,,,, ,,,,W,,,,2,,,,2,,,, ,,,,W,,,,′,,,,2,,,,(,,,,b,,,,b,,,,†,,,,−,,,,b,,,,†,,,,b,,,,),,,,{displaystyle,,,,H={frac,,,,{(p)^{2}}{2}} {frac,,,,{{W}^{2}}{2}} {frac,,,,{W'}{2}}(bb^{dagger,,,,}-b^{dagger,,,,}b)},,,,.,,,,H,,(,,1,,),,ψ,,0,,(,,1,,),,(,,x,,),,=,,A,,†,,A,,ψ,,0,,(,,1,,),,(,,x,,),,=,,A,,†,,(,,ℏ,,2,,m,,d,,d,,x,, ,,W,,(,,x,,),,),,ψ,,0,,(,,1,,),,(,,x,,),,=,,0.,,This,,,site,,,uses,,,cookies,,,to,,,improve,,,performance.,,,

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