High School How Are 2D Standing Waves Extended to 3D in Quantum Mechanics?

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SUMMARY

The discussion focuses on the mathematical extension of 2D standing waves to 3D in quantum mechanics, specifically in the context of electron wave functions around atoms. It highlights that while electrons are described as standing waves with harmonics corresponding to energy levels, their wave functions must account for three spatial dimensions. The conversation suggests researching 3D standing waves and hydrogen orbitals for a clearer understanding of this concept.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with wave functions and their mathematical representations
  • Basic knowledge of 2D and 3D wave phenomena
  • Concept of harmonics in wave mechanics
NEXT STEPS
  • Research the mathematical formulation of 3D standing waves
  • Study hydrogen orbitals and their significance in quantum mechanics
  • Explore the Schrödinger equation in three dimensions
  • Investigate the relationship between wave functions and energy levels in quantum systems
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Students and professionals in physics, particularly those studying quantum mechanics, as well as educators seeking to explain the transition from 2D to 3D wave functions in atomic models.

etotheipi
I’ve seen the description of electrons around an atom as existing as standing waves with different harmonics corresponding to different energy levels.

The atom is evidently 3-dimensional, and the wave function of an electron must also be in terms if 3 spatial coordinates.

What mathematical extension to 2D standing waves is made to convert them i to a 3D form? I’m almost certainly not nearly good enough to understand the full maths behind this but was just wondering where I could find a more high level description of this.

Thanks
 
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Hi ##e^\pi##

Google 3D standing waves to get an idea :smile:
Or hydrogen orbitals

See e.g. here
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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