Angular Momentum Hydrogen Atom Problem: Physically Explained When L=0

In summary, Angular momentum is a measure of rotational motion and plays a crucial role in determining the energy levels and orbitals of the Hydrogen atom. It is related to the principle quantum number and helps explain the stability and quantized nature of the atom's electron orbitals. The concept of Angular Momentum also contributes to our understanding of the discrete energy levels and orbital shapes of the Hydrogen atom.
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LagrangeEuler
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In quantum mechanics hydrogen atom problem ##L=\sqrt{l(l+1)}\hbar##. What that means physically when ##L=0##?
 
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L = 0 is only possible when l = 0 which means that the wave function has no angular dependence and spherically symmetric.
 
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And also for a particle moving in some potential energy other than the hydrogenic ##V\propto 1/r##, the energy eigenfunctions with ##L=0## are spherically symmetric. These systems include the 3D harmonic oscillator ##V(x,y,z) = C(x^2 + y^2 + z^2 )## and the spherical potential well where ##V(r) = 0## if ##r<R## and ##V(r) = V_0## when ##r\geq R##.
 

FAQ: Angular Momentum Hydrogen Atom Problem: Physically Explained When L=0

What is angular momentum in the context of the hydrogen atom problem?

Angular momentum is a measure of the rotational motion of a particle around a fixed point. In the context of the hydrogen atom problem, it refers to the orbital motion of the electron around the nucleus.

How is angular momentum related to the quantum number L?

The quantum number L represents the magnitude of the angular momentum of the electron in the hydrogen atom. It is related to the shape of the electron's orbital and can take on values from 0 to n-1, where n is the principal quantum number.

Why is the angular momentum of the electron quantized in the hydrogen atom?

The angular momentum of the electron is quantized in the hydrogen atom because the electron can only occupy certain discrete energy levels, and each energy level corresponds to a specific value of angular momentum. This is a fundamental principle of quantum mechanics.

How does the value of L affect the energy levels of the hydrogen atom?

The value of L determines the energy levels of the hydrogen atom. As L increases, the energy levels also increase. This is because the higher the angular momentum, the more energy the electron has in its orbital motion.

Can the angular momentum of the electron in the hydrogen atom be changed?

Yes, the angular momentum of the electron can be changed if the electron absorbs or emits energy. This can happen through interactions with other particles or through the absorption or emission of photons. However, the value of L will always be quantized and will correspond to a specific energy level.

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