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Mrinmoy Naskar
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y" - 2xy' + my = 0 this is well known hermite diff eqn. now can anyone tell me what kind of conts is m?? what is the suitable value of m??
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Mrinmoy Naskar said:y" - 2xy' + ny = 0 this is well known hermite diff eqn. now can anyone tell me what kind of conts is m?? what is the suitable value of m??
sorry for the confusion.. I made the correction in my qus...drvrm said:please explain what is 'm'?
Several web pages that I looked at say that m is usually a nonnegative integer. Did you try searching for yourself?Mrinmoy Naskar said:y" - 2xy' + my = 0 this is well known hermite diff eqn. now can anyone tell me what kind of conts is m?? what is the suitable value of m??
Mrinmoy Naskar said:can anyone tell me what kind of conts is m?? what is the suitable value of m??
@mrinmoy Pl. see a detail analysisMark44 said:Several web pages that I looked at say that m is usually a nonnegative integer. Did you try searching for yourself?
The Hermite differential equation is a second-order linear differential equation that is commonly used in mathematical physics. It is named after the French mathematician Charles Hermite and has the form y'' - 2xy' + 2ny = 0, where n is a constant.
The Hermite differential equation has many applications in physics, specifically in quantum mechanics and statistical mechanics. It is used to describe the behavior of quantum harmonic oscillators and the energy levels of certain physical systems.
The Hermite differential equation can be solved using various methods, including power series, Frobenius method, and the Heun method. The solution involves finding the eigenvalues and eigenfunctions of the differential equation, which are used to construct the general solution.
The Hermite differential equation can be used to model the vibrations of diatomic molecules, the motion of a charged particle in a magnetic field, and the behavior of electrons in a crystal lattice. It is also used in statistics to describe the probability distribution of a normal random variable.
Yes, there are various forms of the Hermite differential equation, such as the modified Hermite equation and the generalized Hermite equation. These variations have different coefficients and may have additional terms, but they still follow the basic structure of a second-order linear differential equation.