Understanding the Imaginary Component in Spherical Harmonics

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In summary, the physical interpretation of the imaginary component in spherical harmonics is that it is a phase function that has no physical consequence on its own. The modulus squared of the spherical harmonics excludes the imaginary component, but this is necessary for consistency in the theory. For pure states, the phase factors are factorized through.
  • #1
repugno
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What is the physical interpretation of the imaginary component in the spherical harmonics? I am under the impression that when we sketch the shapes of the spherical harmonics we exclude the imaginary components.
 
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  • #2
We typically do. The wave function itself has no physical interpretation, merely its modulus squared, so by itself the imaginary part is of no physical consequence.

In fact, one can show that the eigenstates of a hamiltonian can always be chosen to be real.
 
  • #3
When we take the modulus squared of the spherical harmonics we loose the term containing the azimuth angle and the imaginary number. Isn't this a problem since we loose information about the shapes?
 
  • #4
The imaginary part of the harmonic is a phase function.
 
  • #5
repugno said:
When we take the modulus squared of the spherical harmonics we loose the term containing the azimuth angle and the imaginary number. Isn't this a problem since we loose information about the shapes?

Consider it a price to be payed in order to keep the theory consistent. As already stated, for pure states phase factors are factorized through.

Daniel.
 

What is the T.I.S.E?

The T.I.S.E stands for the "Time Independent Schrödinger Equation" and is a mathematical equation used in quantum mechanics to describe the behavior of a quantum system over time.

What does the solution to the T.I.S.E represent?

The solution to the T.I.S.E represents the wave function of a quantum system, which describes the probability of finding the system in a particular state at a given time.

How is the T.I.S.E solved?

The T.I.S.E can be solved using various methods, including analytical methods such as separation of variables or numerical methods such as the finite difference method. The specific method used depends on the specific system and boundary conditions.

What is the importance of the T.I.S.E in quantum mechanics?

The T.I.S.E is a fundamental equation in quantum mechanics and is used to describe the behavior of many physical systems, including atoms, molecules, and subatomic particles. It allows scientists to make predictions about the behavior of these systems and has been crucial in the development of modern technology such as transistors and lasers.

Are there any limitations to the T.I.S.E?

Yes, the T.I.S.E has some limitations, particularly in systems with strong interactions or systems with changing potentials. In these cases, more advanced equations such as the time-dependent Schrödinger equation may be used.

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