The spinning period for a free electron and the periods of spin and orbital motion of the electron in an atomic state have been calculated. We have shown that for a free electron the spinning period is: (Ts)free=1.9×10-20s. But in the atomic case we show that, both the spin and the orbital periods depend on the quantum numbers n, ml, ms and the effective Landé-g factor, g* which is a function of the quantum number l of the atomic state given in Dirac notation. We have also calculated these periods for the ground state and some excited states—hydrogen and hydrogen-like atoms. For atomic states the approximate values of spinning period are and the related orbital periods are: (T0)atomic=(10-16-10-15)s. Therefore atto-second processes which are related to the pulse of 10-18 s will filter the orbital motion of the electron but will be long enough to detect the details of the spin motion, such as flip-flops.The spinning period for a free electron and the periods of spin and orbital motion of the electron in an atomic state have been calculated. We have shown that for a free electron the spinning period is: (Ts)free=1.9×10-20s. But in the atomic case we show that, both the spin and the orbital periods depend on the quantum numbers n, ml, ms and the effective Landé-g factor, g* which is a function of the quantum number l of the atomic state given in Dirac notation. We have also calculated these periods for the ground state and some excited states—hydrogen and hydrogen-like atoms. For atomic states the approximate values of spinning period are and the related orbital periods are: (T0)atomic=(10-16-10-15)s. Therefore atto-second processes which are related to the pulse of 10-18 s will filter the orbital motion of the electron but will be long enough to detect the details of the spin motion, such as flip-flops.

Journal of Modern PhysicsJan 1, 20151 citation

Theory of Atomic Structure and Spin of Electron

Mituo Taketani, Masayuki Nagasaki

WORLD SCIENTIFIC eBooksNov 1, 20010 citations

An efficient quantum algorithm for preparing states of molecular systems

Hefeng Wang, Sahel Ashhab, Franco Nori

We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin orbitals. Each spin orbital is mapped to a qubit: the states $| 1 >$ and $| 0>$ of the qubit represent, respectively, whether the spin orbital is occupied by an electron or not. To prepare a general state in the full Hilbert space of $n$ qubits, which is of dimension $2^{n}$ %, $O(2^{n})$ CNOT gates are needed, i.e. the number of gates scales \emph{% exponentially} with the number of qubits. We make use of the fact that the state to be prepared lies in a smaller Hilbert space, and we find an algorithm that requires at most $O((2 n)^{m}/{m!})$ CNOT gates, i.e. scales \emph{polynomially} with the number of qubits $n$ , provided $n\gg m$ . The algorithm is simulated numerically to prepare the electronic states of the hydrogen molecule and the water molecule. We show that when additional symmetries of the system are considered, the number of gates to prepare the state can be reduced dramatically.We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number $m$ of electrons occupying a given number $n$ of spin orbitals. Each spin orbital is mapped to a qubit: the states $| 1 >$ and $| 0>$ of the qubit represent, respectively, whether the spin orbital is occupied by an electron or not. To prepare a general state in the full Hilbert space of $n$ qubits, which is of dimension $2^{n}$%, $O(2^{n})$ CNOT gates are needed, i.e. the number of gates scales \emph{% exponentially} with the number of qubits. We make use of the fact that the state to be prepared lies in a smaller Hilbert space, and we find an algorithm that requires at most $O((2 n)^{m}/{m!})$ CNOT gates, i.e. scales \emph{polynomially} with the number of qubits $n$, provided $n\gg m$. The algorithm is simulated numerically to prepare the electronic states of the hydrogen molecule and the water molecule. We show that when additional symmetries of the system are considered, the number of gates to prepare the state can be reduced dramatically.

Feb 9, 20092 citations

Electron Spin and Proton Spin in the Hydrogen and Hydrogen-Like Atomic Systems

Stanisław Olszewski

The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time.The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae.The quantization of the spin motion has been done on the basis of the old quantum theory.It gives a quantum number n = 1/2 as the index of the spin state acceptable for both the electron and proton particle.In effect of the spin existence the electron motion in the hydrogen atom can be represented as a drift motion accomplished in a combined electric and magnetic field.More than 18,000 spin oscillations accompany one drift circulation performed along the lowest orbit of the Bohr atom.The semiclassical theory developed in the paper has been applied to calculate the doublet separation of the experimentally well-examined D line entering the spectrum of the sodium atom.This separation is found to be much similar to that obtained according to the relativistic old quantum theory.The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time.The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae.The quantization of the spin motion has been done on the basis of the old quantum theory.It gives a quantum number n = 1/2 as the index of the spin state acceptable for both the electron and proton particle.In effect of the spin existence the electron motion in the hydrogen atom can be represented as a drift motion accomplished in a combined electric and magnetic field.More than 18,000 spin oscillations accompany one drift circulation performed along the lowest orbit of the Bohr atom.The semiclassical theory developed in the paper has been applied to calculate the doublet separation of the experimentally well-examined D line entering the spectrum of the sodium atom.This separation is found to be much similar to that obtained according to the relativistic old quantum theory.

Journal of Modern PhysicsJan 1, 20149 citations

Electrons with Spin

Pieter Kok

Undergraduate lecture notes in physicsJan 1, 20180 citations

We present an efficient quantum algorithm for preparing a pure state on a quantum computer, where the quantum state corresponds to that of a molecular system with a given number

m

of electrons occupying a given number

n

of spin orbitals. Each spin orbital is mapped to a qubit: the states

| 1 >

and

| 0>

of the qubit represent, respectively, whether the spin orbital is occupied by an electron or not. To prepare a general state in the full Hilbert space of

n

qubits, which is of dimension

2^{n}

O(2^{n})

CNOT gates are needed, i.e. the number of gates scales \emph{% exponentially} with the number of qubits. We make use of the fact that the state to be prepared lies in a smaller Hilbert space, and we find an algorithm that requires at most

O((2 n)^{m}/{m!})

CNOT gates, i.e. scales \emph{polynomially} with the number of qubits

n

, provided

n\gg m

. The algorithm is simulated numerically to prepare the electronic states of the hydrogen molecule and the water molecule. We show that when additional symmetries of the system are considered, the number of gates to prepare the state can be reduced dramatically.