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...
Code Issues Pull requests Markdown and LaTeX online editor - create text for web with equations and diagrams latex math equation Updated Oct 14, 2024 JavaScript RapidAI / RapidLaTeXOCR Star 301 Code Issues Pull requests Discussions Formula recognition based on LaTeX-OCR and ONNXRuntime. py...
quadratic, quadratic equation - an equation in which the highest power of an unknown quantity is a square biquadratic equation, biquadratic - an equation of the fourth degree differential equation - an equation containing differentials of a function simultaneous equations - a set of equations in two...
Particularly is the fractional differential equations requiring operators with Sonine kernels in a function space C−1(0,+∞) - known as the space of continuous functions on R+ whose integrable singularity of a power function class exists at the origin. Differential equations involving general ...
A general form of a differential equation with periodic coefficients is Hill’s equation: x¨+h(t)x=0 where h(t)=h(t+T). In the particular case in which the periodic function is a cosine we have the Mathieu equation; it is frequently written as (9.2)ϕ¨+(δ+∊cos2t)ϕ=0 ...
A functional is constructed from the spectral density used in the general Gel'fand–Levitan equation and an arbitrary functionNof two sets of variables. Th... M Kanal,HE Moses - 《Journal of Mathematical Physics》 被引量: 15发表: 1977年 On algebraic functions satisfying a class of functional...
with coefficients, that may or may not vary with x, is y=e−a(x)∫g(x)ea(x)dx+κ, where κ is the constant of integration, and a(x)=∫f(x)dx. A compact form of the general solution based on a Green’s function is y(x)=∫ax[y(a)δ(t−a)+g(t)]e−∫txf(...
If a function has more than one independent variable, the total change in the function will depend on more than one variable. In such a case, we are faced with a “partial differential equation” (PDE).Eq. 3.3was an example of a function that depends on more than one independent variable...