Uploaded August 2025 | Updated September 2026, 2 weeks ago
Schrödinger EquationBasic Overview
Dr. DeBacco
Schrödinger Equation
The Schrödinger Equation is a mathematical tool that provides the wave functions and energy levels used in the quantum mechanical model.
Revolutionized the atomic theory.
Schrödinger “Electron Cloud” Model
The cloud represents the probability of where an electron might be found at any given time.
The Cloud Explained
High-density areas of the cloud = high probability of finding an electron
Low-density areas = low probability
The cloud is fuzzy, not fixed, because of the Heisenberg Uncertainty Principle, which says we can't know both the exact position and momentum of an electron simultaneously
Schrödinger Equation
Schrödinger Equation: A mathematical equation developed by Erwin Schrödinger in 1925–1926, forming the foundation of the quantum mechanical model.
Its solutions provide the wave function (ψ) that describe the probability distributions of electrons in orbitals.
For example, solving the Schrödinger equation for a hydrogen atom yields the 1s, 2s, 2p, etc., orbitals, which are central to the model.
Time-independent Schrödinger equation
Specifically, the time-independent Schrödinger equation is used for atoms to find the allowed energy levels and wave functions of electrons.
Solving the Schrödinger Equation
Schrödinger Equation:
Solving yields a set of quantized energy levels:
Where n = 1, 2, 3... is the principal quantum number
Each level corresponds to an orbital with a specific shape and energy
These orbitals (like the famous 1s, 2p, 3d…) define where you're most likely to find the electron—think of them like probability clouds!
This gives rise to quantum numbers and helps explain the complex shape of orbitals.
Described as part of the Quantum Mechanical Model
Helps Explain Spectral Lines
Schrödinger Equation:
It explains spectral lines: when electrons jump between levels, they emit or absorb light at specific wavelengths.
It laid the groundwork for atomic physics, chemistry, and even lasers.
Link to Lecture Slides: drive.google.com/file/d/1R8_-DpWekTROA3_meQO_dXR8iHSXgDCK/view?usp=drive_link
*Due to the description character limit the full work cited for "Schrodinger Equation Basic Overview" can be viewed at... docs.google.com/document/d/1O1LAxH0v2pWl3yrSxwqIUid5ylhlnqN5/edit?usp=drive_link&ouid=104237452697237972847&rtpof=true&sd=true
Schrödinger EquationBasic Overview
Dr. DeBacco
Schrödinger Equation
The Schrödinger Equation is a mathematical tool that provides the wave functions and energy levels used in the quantum mechanical model.
Revolutionized the atomic theory.
Schrödinger “Electron Cloud” Model
The cloud represents the probability of where an electron might be found at any given time.
The Cloud Explained
High-density areas of the cloud = high probability of finding an electron
Low-density areas = low probability
The cloud is fuzzy, not fixed, because of the Heisenberg Uncertainty Principle, which says we can't know both the exact position and momentum of an electron simultaneously
Schrödinger Equation
Schrödinger Equation: A mathematical equation developed by Erwin Schrödinger in 1925–1926, forming the foundation of the quantum mechanical model.
Its solutions provide the wave function (ψ) that describe the probability distributions of electrons in orbitals.
For example, solving the Schrödinger equation for a hydrogen atom yields the 1s, 2s, 2p, etc., orbitals, which are central to the model.
Time-independent Schrödinger equation
Specifically, the time-independent Schrödinger equation is used for atoms to find the allowed energy levels and wave functions of electrons.
Solving the Schrödinger Equation
Schrödinger Equation:
Solving yields a set of quantized energy levels:
Where n = 1, 2, 3... is the principal quantum number
Each level corresponds to an orbital with a specific shape and energy
These orbitals (like the famous 1s, 2p, 3d…) define where you're most likely to find the electron—think of them like probability clouds!
This gives rise to quantum numbers and helps explain the complex shape of orbitals.
Described as part of the Quantum Mechanical Model
Helps Explain Spectral Lines
Schrödinger Equation:
It explains spectral lines: when electrons jump between levels, they emit or absorb light at specific wavelengths.
It laid the groundwork for atomic physics, chemistry, and even lasers.
Link to Lecture Slides: drive.google.com/file/d/1R8_-DpWekTROA3_meQO_dXR8iHSXgDCK/view?usp=drive_link
*Due to the description character limit the full work cited for "Schrodinger Equation Basic Overview" can be viewed at... docs.google.com/document/d/1O1LAxH0v2pWl3yrSxwqIUid5ylhlnqN5/edit?usp=drive_link&ouid=104237452697237972847&rtpof=true&sd=true
