scholarly journals MENENTUKAN PERSAMAAN GELOMBANG SCHR�DINGER POTENSIAL NON-SENTRAL SCARF HIPERBOLIK PLUS ROSEN-MORSE TRIGONOMETRIK MENGGUNAKANMETODE SUPERSIMETRI MEKANIKA KUANTUM

2018 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
M. SYAIFUDIN M. SYAIFUDIN
Keyword(s):  
Raising Operator ◽  
Lowering Operator

Penelitian ini bertujuan untuk menentukan persamaan gelombang Schrdinger potensial non-sentral Scarf hiperbolik plus Rosen-Morse trigonometrik menggunakan metode Supersimetri Mekanika Kuantum (SUSI MK). Persamaangelombang radial diperoleh dari persamaan Schrdinger bagian radial, sedangkan persamaan gelombang sudut diperoleh dari persamaan Schrdinger bagian sudut polar. Penentuan persamaan gelombang tingkat dasar ditentukan dengan sifat lowering operator dan persamaan gelombang tereksitasi ditentukan dengan sifat raising operator. Jadi, baik untuk bagian radial maupun bagian polar ditentukan dengan menggunakan metode operator supersimetri. Adapun tampilan gambar dari fungsi gelombang bagian polar menggunakan aplikasi program maple 12.

scholarly journals Solution of The Schrödinger Equation for Trigonometric Scarf Plus Poschl-Teller Non-Central Potential Using Supersymmetry Quantum Mechanics

2016 ◽  
Vol 4 (01) ◽  
pp. 1 ◽  
Author(s):  
Cari C ◽  
Suparmi S ◽  
Antomi Saregar
Keyword(s):  
Ground State ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
State Wave ◽  
Shape Invariant ◽  
Raising Operator ◽  
Invariant Properties ◽  
Lowering Operator ◽  
Exact Energy

<span>In this paper, we show that the exact energy eigenvalues and eigen functions of the Schrödinger <span>equation for charged particles moving in certain class of noncentral potentials can be easily <span>calculated analytically in a simple and elegant manner by using Supersymmetric method <span>(SUSYQM). We discuss the trigonometric Scarf plus Poschl-Teller systems. Then, by operating <span>the lowering operator we get the ground state wave function, and the excited state wave functions <span>are obtained by operating raising operator repeatedly. The energy eigenvalue is expressed in the <span>closed form obtained using the shape invariant properties. The results are in exact agreement with <span>other methods.</span></span></span></span></span></span></span><br /></span>

The water industry and decarbonisation of cities: A review

2020 ◽  
Vol 07 ◽  
Author(s):  
Peter M.J. Fisher ◽  
David Smith
Keyword(s):  
Water Quality ◽  
Strategic Alliances ◽  
Water Industry ◽  
Water Quality Standards ◽  
Starting Point ◽  
Manufacturing Sectors ◽  
Zero Carbon ◽  
Real Time Tracking ◽  
Raising Operator ◽  
Desalination Plants

: The urban water industry is a very energy intensive industry. Higher water quality standards are driving a level of energy growth that is threatening to move it to the top rank. Climate change is further exacerbating this situation: Growing aridity is variously imposing an enhanced carbon burden through water recycling, trans-regional pipelines and desalination plants. Natural disasters too can often affect water quality requiring energy hungry mitigations. There’s clear evidence that a failure to appropriately weight energy considerations in water infrastructure is commonplace and that this is an unsustainable position for the industry and is prejudicial to working towards zero carbon cities. Real time tracking of CO2e emissions is an important starting point in raising operator consciousness and introducing rivalry between utilities in attaining abatement. So too is reaching out to the resource and manufacturing sectors to form strategic alliances as well as seeking to enter into closer relationships with the energy sector.

On the Dimension of an Irreducible Tensor Representation of the General Linear Group GL(d)

1970 ◽  
Vol 13 (3) ◽  
pp. 389-390
Author(s):  
J. A. J. Matthews ◽  
G. de B. Robinson
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Irreducible Representations ◽  
Young Diagrams ◽  
Tensor Representation ◽  
Irreducible Tensor ◽  
Tensor Representations ◽  
Identity Representation ◽  
Raising Operator ◽  
Image Position

As has long been known, the irreducible tensor representations of GL(d) of rank n may be labeled by means of the irreducible representations of Sn, i.e., by means of the Young diagrams [λ], where λ1 + λ2 + … λr = n. We denote such a tensor representation by 〈λ〉. Using Young's raising operator Rij we can write [1, p. 42]1.1where the dot denotes the inducing process. For example, [3] . [2] is that representation of S5 induced by the identity representation of its subgroup S3 × S2.

PARASUPERSYMMETRIC COHERENT STATES FOR LANDAU LEVELS WITH DYNAMICAL SYMMETRY GROUP H4

2002 ◽  
Vol 17 (28) ◽  
pp. 4081-4093 ◽  
Author(s):  
H. FAKHRI ◽  
H. MOTAVALI
Keyword(s):  
Magnetic Field ◽  
Symmetry Group ◽  
Coherent States ◽  
Ad Hoc ◽  
Flat Surface ◽  
Arbitrary Order ◽  
Dynamical Symmetry ◽  
Quantum States ◽  
Landau Levels ◽  
Lowering Operator

The eigenstates and their degeneracy for parasupersymmetric Hamiltonian of arbitrary order p, corresponding to the motion of a charged particle with spin [Formula: see text] on the flat surface in the presence of a constant magnetic field along z-axis, are calculated. The eigenstates are expressed in terms of Landau levels quantum states with dynamical symmetry group H4. Furthermore, parasupersymmetric coherent states with multiplicity degeneracy are derived for an ad hoc lowering operator of the eigenstates in terms of ordinary coherent states of Landau Hamiltonian.

A Note on Young's Raising Operator

1981 ◽  
Vol 33 (1) ◽  
pp. 49-54 ◽  
Author(s):  
Glânffrwd P. Thomas
Keyword(s):  
Schur Functions ◽  
Homogeneous Product ◽  
Raising Operator ◽  
Image Position

Consider the following formula due to Young [7] for the calculation of the homogeneous product sum, hλ, in terms of Schur functions;where the operation Srs is defined as follows:Y1: Srs, where r < s, “represents the operation of moving one letter from the s-th row up to the r-th row; and the resulting term is regarded as zero, when any row becomes less than a row below it, or when letters from the same row overlap; as, for instance, happens when λ1 = λ2 in the case of S13S23.“The following example of the above is given by Robinson [4].Calculation by other means shows that the above analysis of h(3,2,1) is correct; however, it will be noticed that the operator S123S23 does not appear in the above yet it is not specifically excluded by the rule Y1.

scholarly journals Linearization coefficients for Sheffer polynomial sets via lowering operators

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Y. Ben Cheikh ◽  
H. Chaggara
Keyword(s):  
Linearization Coefficients ◽  
Lowering Operators ◽  
Sheffer Polynomial ◽  
Lowering Operator

The lowering operatorσassociated with a polynomial set{Pn}n≥0is an operator not depending onnand satisfying the relationσPn=nPn−1. In this paper, we express explicitly the linearization coefficients for polynomial sets of Sheffer type using the corresponding lowering operators. We obtain some well-known results as particular cases.

scholarly journals NEW DISCRETE STATES IN TWO-DIMENSIONAL SUPERGRAVITY

2007 ◽  
Vol 22 (07) ◽  
pp. 1375-1394 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Operator Algebra ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Field Theories ◽  
Two Dimensional ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving ◽  
Volume Preserving ◽  
Lowering Operator

Two-dimensional string theory is known to contain the set of discrete states that are the SU (2) multiplets generated by the lowering operator of the SU (2) current algebra. Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. In this paper we show that the interaction of d = 2 superstrings with the superconformal β - γ ghosts enlarges the actual algebra of the dimension 1 currents and hence the new ghost-dependent discrete states appear. Generally, these states are the SU (N) multiplets if the algebra includes the currents of ghost numbers n : -N ≤ n ≤ N - 2, not related by picture changing. We compute the structure constants of these ghost-dependent discrete states for N = 3 and express them in terms of SU (3) Clebsch–Gordan coefficients, relating this operator algebra to the volume preserving diffeomorphisms in d = 3. For general N, the operator algebra is conjectured to be isomorphic to SDiff (N). This points at possible holographic relations between two-dimensional superstrings and field theories in higher dimensions.

scholarly journals L-classical d-orthogonal polynomial sets of Sheffer type

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 881-895
Author(s):  
Youssèf Cheikh ◽  
Inès Gam
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomial ◽  
Order Differential Equation ◽  
Derivative Operator ◽  
Classical Orthogonal Polynomial ◽  
First Case ◽  
Lowering Operators ◽  
Lowering Operator

In this paper, we characterize L-classical d-orthogonal polynomial sets of Sheffer type where L being a lowering operator commutating with the derivative operator D and belonging to {D,eD-1, sin(D)}. For the first case we state a (d+1)-order differential equation satisfied by the corresponding polynomials. We, also, show that, with these three lowering operators, all the orthogonal polynomial sets are classified as L-classical orthogonal polynomial sets.

scholarly journals HAHN'S PROBLEM WITH RESPECT TO SOME PERTURBATIONS OF THE RAISING OPERATOR \(X-c\)

2020 ◽  
Vol 6 (2) ◽  
pp. 15
Author(s):  
Baghdadi Aloui ◽  
Jihad Souissi
Keyword(s):  
Orthogonal Polynomial ◽  
Complex Number ◽  
Classical Orthogonal Polynomial ◽  
Arbitrary Complex Number ◽  
Raising Operators ◽  
Charlier Polynomial ◽  
Arbitrary Complex ◽  
Raising Operator

In this paper, we study the Hahn's problem with respect to some raising operators perturbed of the operator \(X-c\), where \(c\) is an arbitrary complex number. More precisely, the two following characterizations hold: up to a normalization, the \(q\)-Hermite (resp. Charlier) polynomial is the only \(H_{\alpha,q}\)-classical (resp. \(\mathcal{S}_{\lambda}\)-classical) orthogonal polynomial, where \(H_{\alpha, q}:=X+\alpha H_q\) and \(\mathcal{S}_{\lambda}:=(X+1)-\lambda\tau_{-1}.\)

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