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Titan97
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In a hydrogen atom, the wave function is written as R(r).Θ(θ).Φ(φ). But how is it separable when the electron is interacting with the nucleus?
The "separability" refers to the form of the partial differential equation (Schrodinger's equation for the ##1/r## potential) we're trying to solve. You can show by substitution that a function of the form ##\psi=R(r)Y(\theta,\phi)## will be a solution. When you make this substitution two separate and simpler differential equations, one for ##R(r)## and the other for ##Y(\theta,\phi)##, will emerge.Titan97 said:In a hydrogen atom, the wave function is written as R(r).Θ(θ).Φ(φ). But how is it separable when the electron is interacting with the nucleus?
Titan97 said:@Nugatory I am asking how can one be sure that a function f(x,y,z)=f(x)f(y)f(z)?
Titan97 said:@Nugatory I am asking how can one be sure that a function f(x,y,z)=f(x)f(y)f(z)?
Titan97 said:I am asking how can one be sure that a function f(x,y,z)=f(x)f(y)f(z)?
Titan97 said:In a hydrogen atom, the wave function is written as R(r).Θ(θ).Φ(φ). But how is it separable when the electron is interacting with the nucleus?
The concept of "Separability of variables" is a mathematical technique used to solve differential equations. It involves breaking down a complex equation into simpler equations that only involve one variable each, making the equation easier to solve.
"Separability of variables" is important in science because many physical phenomena can be described by differential equations. By using this technique, scientists can solve these equations and gain a better understanding of the underlying mechanisms and behavior of the system being studied.
The process of "Separability of variables" involves isolating each variable on one side of the equation and integrating both sides separately. This results in a solution that satisfies the original equation and can be used to make predictions and analyze the system.
One limitation of "Separability of variables" is that it can only be applied to certain types of differential equations, specifically those that can be written in a separable form. Additionally, it may not always be possible to find an exact solution using this technique, and numerical methods may be required.
Yes, "Separability of variables" can be applied to real-world problems in various fields such as physics, chemistry, and engineering. It is a powerful tool that allows scientists to model and understand complex systems and make predictions about their behavior.