Schrodinger Equation
Definition and meaning of Schrodinger Equation in chemistry.
The Schrodinger equation is a fundamental mathematical equation in quantum mechanics that describes the wave function of a quantum system over time. It allows chemists to calculate the probability of finding an electron in a specific region of space around an atomic nucleus.
In more detail
Formulated by Austrian physicist Erwin Schrodinger in 1926, this equation is the quantum mechanical equivalent of Newton's laws of motion. While classical physics uses equations to predict the exact path of a moving object, the microscopic world does not behave predictably. Because electrons act as both particles and waves, their exact positions and speeds cannot be known simultaneously.
Instead, the Schrodinger equation uses complex mathematics to define an electron's behavior in terms of probabilities, successfully replacing the idea of fixed orbits with three-dimensional probability maps known as orbitals. The equation comes in two main forms: the time-dependent and the time-independent Schrodinger equation. In most chemical applications, the time-independent form is utilized to find the stationary states or allowed energy levels of a stable molecule.
Solving the equation yields the wave function, commonly represented by the Greek letter psi. When this mathematical wave function is squared, it provides the probability density. This density illustrates where an electron is most likely to be found, creating the familiar shapes of s, p, d, and f orbitals that dictate all chemical bonding.
Although the equation can be solved exactly for a simple system like the hydrogen atom, it becomes incredibly complex for atoms with multiple electrons due to complicated electron-electron repulsions. To study larger molecules, chemists rely on powerful supercomputers and various mathematical approximations, such as the Born-Oppenheimer approximation, to estimate the solutions.
These computational methods form the absolute basis of modern computational chemistry, allowing scientists to model molecular structures, predict chemical reactions, and design new drugs without needing to perform every experiment in a physical laboratory.
Key facts
| Field | Physical Chemistry |
|---|---|
| Formulated By | Erwin Schrodinger |
| Year Published | 1926 |
| Calculates | Wave Functions |
| Quantum Concept | Probability Density |
| Key Symbol | Psi |
| Approximation Used | Born-Oppenheimer Approximation |
By solving the Schrodinger equation for a single hydrogen atom, chemists can perfectly mathematically derive the spherical shape of the 1s orbital, which shows where the atom's lone electron spends most of its time.
Frequently asked questions
Can the Schrodinger equation be solved exactly for any molecule?
No, it can only be solved exactly for one-electron systems like the hydrogen atom; everything else requires complex mathematical approximations.
What does squaring the wave function tell you?
Squaring the wave function gives the probability density, which is the actual likelihood of finding an electron at a specific point in three-dimensional space.
How did this equation change chemistry?
It proved that electrons do not orbit the nucleus in flat, planetary rings, but rather exist in three-dimensional probability clouds called orbitals.