The law of conservation of energy is one of Newton’s primary laws, which states that energy can neither be created nor destroyed. Schrodinger’s equation plays the role of Newton’s laws and conservation of energy by predicting the future behavior of a dynamic system. It clears the air and clarifies the crux of the conservation of energy aspect. The equation is a wave function that predicts the probability of events or outcomes. The detailed outcome is not strictly determined; however, Schrodinger’s equation is widely used to predict the distribution of results.
Who is Schrodinger?
Erwin Schrodinger was an Austrian theoretical physicist who contributed to the wave theory of matter and other aspects of quantum mechanics. For his wide array of contributions, he was awarded the Nobel prize for his contributions in 1933, which was shared by another British physicist.
Schrodinger obtained his doctorate from the University of Vienna in 1906, which helped him to accept a research post at the university’s second physics institute. He served the military in World War one and went to the University of Zurich in 1921. He was such a determined person that he published papers that paved the foundations of quantum wave mechanics well past his retirement. In his work, he described the partial differential equation that has a relationship between the equation of quantum mechanics and mechanics of the atom.
A Quick Brush up
Through the work of Albert Einstein and Max Plank, we have learnt that energy is quantized, and light exhibits wave-particle duality. Quantized energy means that the system can have only certain energies and not a continuum of energies. For instance, only certain speeds at which a car can travel due to its kinetic energy could be having only certain values. Physicist Louis de Broglie extended this duality to include matter, which is that all matter possesses a wavelength. Regardless of it being a tiny electron, a whole body, or a huge star.
An object’s wavelength is inversely proportional to its mass, which means that macroscopic objects have very tiny wavelengths. However, since an electron is so small, its wavelength becomes relevant, which is being around the size of an atom. Therefore, we can conclude that electrons can behave like waves and particles.
Wave-nature of an Electron
An electron can be regarded as a standing wave but not a linear wave. It is a circular standing wave that surrounds the nucleus. This helps us understand why the quantization of the energy of the electron is clear. This is because any circular standing wave can only have an integer number of wavelengths. With the increasing number of wavelengths, more energy will be carried by the wave. An electron in an atom can only have a discreet number set of energy levels.
When an electron strikes a proton of a particular energy, this energy is absorbed, promoting the electron to a higher energy state and increasing the number of wavelengths—contained within the standing wave.
Here, the constructive equivalence of standing waves results in covalent bonding through orbital overlap. When it was realized that electrons exhibit wave behavior, physicists were keen on finding a mathematical model that describes this behavior. In 1925, Erwin Schrodinger achieved this goal with his signature equation.
The Schrodinger’s Equation
Schrodinger’s equation is a differential equation that is hard to decipher and cannot be explained in this article as it contains arithmetic. However, let us look into the conceptual aspect of this equation. Just like how Newton’s second law states that force equals mass into acceleration, the Schrodinger equation is applicable to quantum systems by describing a system’s three-dimensional wave function, which is represented by psi.
H represents the Hamiltonian operator, a set of operations that describe all interactions that impact the system’s state. This refers to the total energy of a particle. Although this calculates the wave function, it doesn’t describe what the wave function is. Physicist Max Born proposed that the wave function has to be interpreted as a probability amplitude. The symbol Ψ tells the probability of an electron found in a particular spot.
In the double-slit experiment, the diffraction pattern illustrates the wave of probability clearly. This pattern illustrates the probability of an electron arriving at any given spot. Bear in mind that the exact location of where an electron will land cannot be predicted; only the probability of arrival at a location can be deciphered. If many electrons arrive, it is apparent that their distribution obeys the wave function.
Schrodinger’s equation computes the wave function deterministically, but the information it contains is probabilistic. This concept of the probabilistic nature of computation was a lot to handle for the scientific community to handle and still continues to be. Just like how sound waves are oscillations in an electromagnetic field, and sound waves are mechanical waves, an electron can be considered as clouds of probability density.
Interpretations of Quantum Mechanics
Schrodinger conceived this equation that helped in interpreting some concepts in quantum mechanics. There were many other physicists who interpreted quantum mechanics, some of which include Copenhagen Interpretation, many-worlds interpretation, Quantum decoherence, and Bohmian Mechanics. These interpretations are different ways of relating the wave function to experimental results and the fundamental beliefs about nature.
Conclusion
The development of quantum mechanics has surely come a long way since Schrodinger’s time, and the recent developments have made a big change in today’s scientific community. Schrodinger’s equation has paved the way for physicists to delve deeper into quantum mechanics and particle physics. Scientists can decipher the interactions of various types of particle matter and compound elements through extensive research.
Space Age 