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• W2967387429 abstract "We study how can an angular momentum coherent state <?CDATA $| tau rangle $?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mo stretchy=false>∣</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=false>〉</mml:mo> </mml:math> keeps its form-invariant during time evolution governed by the Hamiltonian <?CDATA $H=f(t){J}_{+}+{f}^{* }(t){J}_{-}+g(t){J}_{z}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>H</mml:mi> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:msub> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:msub> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:msub> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> </mml:msub> </mml:math> . We discuss this topic in the context of boson realization of <?CDATA $| tau rangle $?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mo stretchy=false>∣</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=false>〉</mml:mo> </mml:math> . By employing the entangled state representation <?CDATA $| zeta rangle $?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mo stretchy=false>∣</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo stretchy=false>〉</mml:mo> </mml:math> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <?CDATA $langle zeta | tau rangle $?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mo stretchy=false>〈</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo stretchy=false>∣</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=false>〉</mml:mo> </mml:math> , which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of <?CDATA $tau (t)$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi>τ</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:math> is totally determined by the parameters involved in the Hamiltonian." @default.
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• W2967387429 date "2019-09-01" @default.
• W2967387429 modified "2023-10-12" @default.
• W2967387429 title "Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem*" @default.
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