General formulae for solutions of the Schrodinger equation with power potentials are derived. The wavefunctions are expressed as products of the asymptotic factors and special forms of the Hessenberg determinants, in general, of infinite order. Conditions under which the order of the determinants ...
6. Week 15 Wave function, Schrodingger equation, infinite deep potential well in one dimension. Spin of electron, forth quantum number, description of hydrogen atom with quantum mechanics, Pauli exclusion principle, shell distribution of electrons out of atomic nucleus. ...
FAQ: Differential equation with power series What is a power series? A power series is an infinite series of the form ∑n=0∞ an(x-c)n, where an are constants and c is a fixed point. It is a type of Taylor series that represents a mathematical function as a sum of powers of (x...
This paper shows a way of deriving a Mincer-type earnings function from the more standard assumption of utility maximization. The implications are less questionable. The approach allows one to analyse the efficiency of education policy in Ramsey's tradition. Distortive wage taxation is shown to ...
With a transient heat transfer, the temperature is a function not only of the space coordinates but of time as well. Equation [18], with suitable boundary and initial conditions, represents the 3D temperature distribution at any time and at any point in the workpiece. The initial temperature ...
For the function(4)γ(k)=(ω2+∑j=122λj(1−coskj))1/2,k=(k1,k2)∈[−π,π]2, introduce(5)I(t,x,η)=1(2π)2∫[−π,π]2ei(k⋅x−tγ(k))η(k)dk, where x∈Z2, t∈R, and η is a smooth test function on [−π,π]2 with periodic boundary ...
Eventually, in the particular case of two spatial dimensions, the exact form of the ground-state wave function is obtained for a potential containing a finite number of inverse powers of r , with the associated energy eigenvalue. 展开
This paper presents an analysis of the evolution of the probability density function of the dynamic trajectories of a single machine infinite bus power system. The probability density function can be used to determine the impact of random (stochastic) load perturbations on system stability. The evolu...
compatibility with equations that were written in a version earlier than Office 2007. Users who want to disable the Equation Editor component can manually create and set registry entries for Microsoft Office. If you do so, some equation objects may not function correctly or be available to the ...
Using the MATLAB function, fzero, the local roots of any one-dimensional equation can be found. To use this command, a separate function file should be created with the title file–name.m. The use of command fzero(‘file–name’,xo) identifies the local root where the function equals ze...