Discussion of the He-He interaction energy in the average energy approximation

Using the Unsöld average energy method a double perturbation theory expression for the interaction energy through second order is obtained which includes intra-atomic correction terms arising from the use of trial wavefunctions to represent the non-interacting molecules. These formal expressions are applied to the ground state He-He interaction and results for the interaction energy are obtained that compare favourably with recent semiempirical and ab initio calculations. The Unsöld calculations are used to investigate approximations that have been introduced into the average energy calculation by other workers, and as a model for discussing the relative importance of second-order charge overlap and exchange effects and the convergence of the multipole treatment of the interaction energy for this typical non-bonded interaction. The results illustrate the importance of knowing as many terms as possible in the R ^-1 expansion of the energy. Finally a portion of this work required the recalculation of the He-He repulsive energy obtained by using the Eckart wavefunction to represent the helium atom. The resultant energy is approximately 25 per cent lower than that previously obtained using this wavefunction for most values of R.     

Structural control of Fano resonances in semiconductor heterostructures

Structural control of quantum interference in the optical intrasubband absorption spectrum of GaAs/AlGaAs multi-quantum wells is investigated theoretically. Our study shows that pronounced Fano resonances are in general difficult to obtain in quantum well heterostructures, with a presence of distinct Fano resonance features being the exception rather than the rule. Guided by an analogy to Young’s double-slit experiment, we design increasingly improved structures to display Fano resonances. Best results are achieved in structures where there is strong overlap between the ground-state wavefunction and scattering states associated with the uncoupled continuum. Alternatively one may use ionization via two or more resonances. In this case, resonances should not be separated by more than 25 meV to give significant effects. Moreover, we show that resonance features may also be induced without potential barriers to a continuum merely via orthogonality between bound and excited states.     

Analysis of multi-configuration density functional theory methods: theory and model application to bond-breaking

We consider the extension of the standard single-determinant Kohn–Sham method to the case of a multi-configuration auxiliary wave function. By applying the rigorous Kohn–Sham method to this case, we construct the proper interacting and auxiliary energy functionals. Following the Hohenberg–Kohn theorem for both energy functionals, we derive the corresponding multi-configuration Kohn–Sham equations, based on a local effective potential. At the end of the analysis we show that, at the ground state, the auxiliary wavefunction must collapse into a single-determinant wave function, equal to the regular KS wavefunction. We also discuss the stability of the wavefunction in multi-configuration density functional theory methods where the auxiliary system is partially interacting, and the remaining (residual) correlation is evaluated as a functional of the density. As an example showing both the challenges and the possibilities, we implement such a procedure for the perfect pairing wavefunction, using a residual correlation functional that is based on the Lee–Yang–Parr functional, and present results for an elementary bond-breaking process.     

Collisional polarizability anisotropies of the noble gases

We present a simple approximate calculation of the pair polarizability anisotropy β(R) of interacting inert gas atoms, including overlap effects. The overlap contribution to β(R) is found to be relatively long-range and to have an exponential form. We compare our results with recent ab initio Hartree-Fock calculations and experimental low density depolarized scattering spectra; agreement is excellent.     

A unified semiclassical description of elastic scattering by a central field

The diffraction-integral formulation of the semiclassical limit of the quantal wavefunction, as proposed in an earlier paper, is applied to the treatment of elastic scattering by a general central-field potential. Angular-momentum quantisation is shown to be a natural consequence of the theory and partial-wave series representations of the s-matrix and asymptotic wavefunction are derived. In addition, the method and results establish a connection between refractive, diffractive, dynamical and uniform-approximation theories of semiclassical scattering.     

General interaction quenches in a Luttinger liquid

We discuss a general interaction quench in a Luttinger liquid described by a paired bosonic Hamiltonian.By employing su(1,1)Lie algebra,the post-quench time-evolved wavefunctions are obtained analytically,from which the time evolution of the entanglement in momentum space can be investigated.We note that depending on the choice of Bogoliubov quasiparticles,the expressions of wavefunctions,which describe time-evolved paired states,can take different forms.The correspondence between the largest entanglement eigenvalue in momentum space and the wavefunction overlap in quench dynamics is discussed,which generalizes the results of Dora et al(2016,Phys.Rev.Lett.117,010603).A numerical demonstration on an XXZ lattice model is presented via the exact diagonalization method.     

Exclusion principle and nuclear reaction mechanism

Effects of the Exclusion Principle in specific reference to direct reactions are studied in detail by formulating a simple one-dimensional model in the two channel approximation. The fact that a target wavefunction can be described by different systems of cluster wavefunctions on account of the indistinguishability of nucleons is exploited to bring out the connections between the various aspects of the reaction mechanism and the forward and the backward reaction amplitudes. The coupled integro-differential equations of the model are solved by a matrix method, and an iteration method respectively for low and high energies of the incident particle in the entrance channel. The exact solution of the coupled integro-differential equations takes into account the Exclusion Principle and the effects of rescattering and target recoil. The result shows that the direct reactions are long distance or “surface” phenomena. An evidence is presented that this is a consequence of the Exclusion Principle. The exact result is compared with various approximate results. The latter include the cases; 1. antisymmetrization is completely neglected; 2. antisymmetrization is performed on the target wavefunctions only; 3. plane wave Born approximation; 4. distorted wave Born approximation. The result obtained by target antisymmetrization coincides with the exact result only for high energies of the incident particle. The practical use of this result obtained by use of the two equivalent clusterwavefunctions which describe the target wavefunction is discussed in connection with heavy particle stripping.     

Approximate formulae for the overlap integral of two harmonic oscillator wave functions

The use of second-order perturbation theory to derive approximate formulae for the overlap integral of two harmonic oscillator wave functions is discussed, and the results applied to the theory of intensity distributions in vibrational progressions in electronic spectra. For the vibrational progression m←0 an approximate formula is given which, when the vibrational frequencies of the initial and final states differ by less than 10%, reproduces to an accuracy of 1% or less the intensity profile calculated using the exact formulae for the overlap integrals.     

GaP中替代缺陷对的A1对称性深能级波函数

本文在Koster-Slater格林函数方法和在位(onsite)势近似的基础上,提出了一个计算替代杂质对的完整方法,并成功地应用于GaP中O替代杂质对。第一次给出了O-Zn和O-Cd对的波函数。我们发现波函数主要集中在O周围4个格点并指向O的化学键上。然而在这4个键上,波函数的分量并不相等,在O—杂质键上的分量要比其它键上的值小。杂质的排斥势越大,则分量值的不平衡越明显。而波函数的其余部分较为平坦地分布在一相当大的空间内。 关键词： GaP     

Optic and acoustic plasmon modes of a semiconductor superlattice

The collective plasmon modes of s semiconductor superlattices consisting of alternating layers of electrons and holes or alternating layers of electrons with different densities are investigated. For wells widely separated in space, such that Bloch wavefunction overlap between wells is negligible, we find optical-like and acoustical-like plasmon modes propagating along the superlattice direction. Perpendicular to the superlattice direction, the acoustic mode (ω～q_″) recently observed by Olego and Pinczuk⁸ is found to be split into two acoustic branches.     

A theoretical study of the 21Ag ← 11Ag two-photon transition and its vibronic band in trans-stilbene

The two-photon spectrum of the 2¹A_g ← 1¹A_g transition in trans-stilbene has been calculated at the complete active space self-consistent field (CASSCF) level of theory. Energies were obtained at the complete active space second-order perturbation (CASPT2) level of theory, while the geometries of both the initial and final states were optimized at the CASSCF level. The energy and the geometry optimizations were performed using an active space of 14 electrons in 14 active π orbitals. The vibrational frequencies of both states and the two-photon transition (TPT) cross-section were calculated with a smaller active space where the two lowest π orbitals were kept inactive. A newly implemented algorithm, in the quantum chemical package Molcas was used to determine the two-photon transition intensity. This method requires only the linear response of the CASSCF wavefunction. Furthermore, the vibronic structure of this TPT was studied. The Franck-Condon factors were obtained by calculating the overlap between the vibrational states involved, which were determined from the force fields of both the initial and final states, at the CASSCF level of theory. The results are in agreement with experiment.     

Generation of displaced squeezed superpositions of coherent states

We study the method of generation of states that approximate superpositions of large-amplitude coherent states (SCSs) with high fidelity in free-traveling fields. Our approach is based on the representation of an arbitrary single-mode pure state, and SCSs in particular, in terms of displaced number states with an arbitrary displacement amplitude. The proposed optical scheme is based on alternation of photon additions and displacement operators (in the general case, N photon additions and N − 1 displacements are required) with a seed coherent state to generate both even and odd displaced squeezed SCSs regardless of the parity of the used photon additions. It is shown that the optical scheme studied is sensitive to the seed coherent state if the other parameters are unchanged. Output states can approximate either even squeezed SCS or odd SCS shifted relative to each other by some value. This allows constructing a local rotation operator, in particular, the Hadamard gate, which is a mainframe element for quantum computation with coherent states. We also show that three-photon additions with two intermediate displacement operators are sufficient to generate even displaced squeezed SCS with the amplitude 1.7 and fidelity more than 0.99. The effects deteriorating the quality of output states are considered.     

The intermolecular potential of HF

The functional form of separate contributions to the intermolecular potential between small dipolar molecules has been analysed using the HF intermolecular potential as an example. The SCF energy was partitioned into first order electrostatic and exchange terms and higher order terms, called the polarization energy, which can be obtained by iterating the wavefunction to self consistency. A comparison was made for each term between a bipolar expansion about a single centre in each molecule and spherically symmetric site-site models. The overlap dependent part of the electrostatic energy could be combined with the exchange energy to give a single term which we call the repulsion energy and this was most accurately represented by a six term bipolar expansion. The polarization energy has a long range (R ^-6) component and an overlap dependent component and both could be separately represented by a two-term bipolar expansion. A semiempirical estimate was made of the dispersion energy and the total potential predicts a geometry of the HF dimer in good agreement with experiment. The predicted binding energy of the dimer is 17 kJ mol^-1 which is slightly smaller than a previous empirical estimate (23 kJ mol^-1).     

Vibration-rotation wavefunctions and energies for any molecule obtained by a variational method

This paper presents an alternative method to the usual approach via perturbation theory for the determination of vibrational-rotational energy levels of a molecule in a given electronic state. It is assumed that the electronic Born-Oppenheimer equation has been solved, by an ab initio method, to give a potential function which is used in the nuclear Born-Oppenheimer equation. But the method can also be used with any potential obtained by any method. An approximate solution to the nuclear equation is derived in the form of a linear combination of expansion functions, the coefficients being determined by the standard linear variational method. Angular momentum theory is used to show that the nuclear wavefunction for m = 0 can be represented by a linear combination of functions of the form

where qi are variables which are closely related to the vibrational normal coordinates, and β, γ are two of the Euler angles. m is the eigenvalue of the Z-component of angular momentum operator in space-fixed axes OXYZ. The H_vi (qi) denote Hermite polynomials while Y^J8 (β, γ) are spherical harmonics. It is explicitly shown how all the matrix elements can be evaluated using a (3N–6) dimensional numerical integration technique. The theory in its present form is not suitable for molecules which are linear in the equilibrium configuration. In the following paper the method is used in a calculation on the water molecule.     

New Trajectory Interpretation of Quantum Mechanics

It was shown by de Broglie and Bohm that the concept of a deterministic particle trajectory is compatible with quantum mechanics. It is demonstrated by explicit construction that there exists another more general deterministic trajectory interpretation. The method exploits an internal angular degree of freedom that is implicit in the Schrödinger equation, in addition to the particle position. The de Broglie-Bohm model is recovered when the new theory is averaged over the internal freedom. The model exhibits a strong form of entanglement which implies a primary role for the wavefunction of the Universe. The conditions of autonomy are examined, and the viability of the theory is established by application to the measurement problem.     

How to build optimal subsets of hyperspherical harmonics

After a short revue of the resolution of few body problems with the hyperspherical harmonics formalism, we develop a method to generate an “optimal subset” of basis functions that approximate the exact wavefunction up to third order of perturbations. Examples are given for three-body systems, with emphasis on the hypertriton. In this latter case, numerical results show that our optimal subset gives an energy some 40 keV higher than that found using a complete set of hyperspherical harmonics.     

Conjectured superfluidity of deuterium

It is proposed that supercooled deuterium may suffer a phase change to the superfluid state near 3 K. A rough estimate of the possibility of the d(d, n)α³ fusion reaction due to large wavefunction overlap in the bose condensate is found to be infinitesimally small.