Why Does the Hydrogen-Atom Wave Function Equal R(r)cita(cita)phi(phi)?

In summary, the hydrogen-atom wave function is a mathematical description of the probability of finding an electron in a particular location around a hydrogen atom. It is calculated using the Schrödinger equation and provides information about the electron's position and energy. It is affected by factors such as the electron's energy level, atomic orbitals, and the presence of other electrons. This function is important in chemistry as it helps us understand atomic behavior and predict chemical bonding and reactions.
  • #1
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why does it equal R(r)cita(cita)phi(phi)?
 
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  • #2
Beforehand there is nothing that tells you it does before you solve the Shrodinger equation. It is just lucky that the problem falls into the class of differential equations known as "seperable equations". You know that it does equal [itex]R(r)\Theta (\theta) \Phi (\phi)[/itex] because it ends up working in the equation.
 
  • #3
Because the Schrödinger equation for the hydrogen atom (a partial differential equation in the three variables [itex]r, \theta, \phi[/itex] is separable into three ordinary differential equations, one for each variable.
 
  • #4
thank you very much!
 

Related to Why Does the Hydrogen-Atom Wave Function Equal R(r)cita(cita)phi(phi)?

What is a hydrogen-atom wave function?

A hydrogen-atom wave function is a mathematical description of the probability of finding an electron in a particular location around a hydrogen atom. It takes into account both the position and energy of the electron.

How is the hydrogen-atom wave function calculated?

The hydrogen-atom wave function is calculated using the Schrödinger equation, which is a mathematical equation that describes how the wave function of a system changes over time.

What does the hydrogen-atom wave function tell us about the electron?

The hydrogen-atom wave function provides information about the electron's position and energy. It can tell us the most probable location of the electron and the likelihood of finding it at a specific distance from the nucleus.

What factors affect the hydrogen-atom wave function?

The hydrogen-atom wave function is affected by the electron's energy level, the shape of the atomic orbitals, and the presence of other electrons in the atom. The wave function also changes as the electron moves around the nucleus.

Why is the hydrogen-atom wave function important in chemistry?

The hydrogen-atom wave function is important in chemistry because it helps us understand the behavior and properties of atoms. It provides a way to predict the likelihood of finding an electron in a certain location, which is crucial in understanding chemical bonding and reactions.

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