Background of Quantum Mechanics
The journey started from Planck’s introduction of quanta in 1900. Planck used the idea to make the classical theory work for black body radiation. He argued that whatever absorbs and emits light, absorbs and emits them at integer multiples of certain amount of energy.
Later in 1905, Einstein extended the idea in his paper on the photoelectric effect where he suggested the quantum concept introduced by Planck is due to the fact that light is grainy.
In 1911, Walther Nernst declared the theory had become “so fruitful” that requires further attention. He went on to say, “it is the duty of science to take it seriously and to subject it to careful investigation”. He managed a conference and gathered leading scientists of the time and urged them to examine this theory more closely. This event proved to be very successful and generated much excitement in the field.
Upon his return from the conference, Nobel laureate Ernest Rutherford discussed the conference with Niels Bohr,who had recently joined Rutherford’s lab. All this excitement caused those who were not present at the conference to also become interested.One such person was then 19-year-old Louis de Broglie, who had been convinced to convert to physics from civil service merely due to the excitement from the proceedings of the conference.
In another paper in 1916, Einstein added to his previous idea suggesting that light is absorbed and emitted in physically real quanta, having momentum and direction. He found himself having to compromise, however, when he realized that introducing statistics and probability was required to make the theory work (which he considered to be a big sacrifice). Nevertheless, he had hoped this would only be a temporary formulation and that it would soon be replaced by some deeper understanding of the concept.
Of course, at this time quantum theory consisted of a loosely related group of hypotheses and theorems which were only of interest to those deeply specialized in the field. This held true until 1925 when two major breakthroughs from Werner Heisenberg and Erwin Schrodinger generalized many of these concepts. In “On the Quantum-Mechanical Reinterpretation of Kinematic and Mechanical Relations”, Werner Heisenberg provided a method for calculating quantum states that did not involve particles or waves. This method used matrices and was called ”matrix mechanics”. However, matrix mechanics was considered difficult to use and almost impossible to visualize, causing resistance from many physicists.
On the other hand, Schrodinger’s work (while covering the same concepts) used the already familiar tools of classical mechanics. He developed a wave equation with continuous functions that unfolded in space and time.
In 1921 Schrodinger was a new lecturer at University of Zurich where he was asked to deliver a formal talk. In his talk, which was called “What is a natural law?”, he suggested the possibility that “the laws of nature without exception have a statistical character”.
In the fall of 1925, Dutch physicist Debye asked Schrodinger to report on the published thesis of de Broglie. This was the paper in which de Broglie used Planck’s rule E = hν to connect momentum of the electron with wavelengths. Schrodinger explained how de Broglie’s idea worked,with the right orbits being obtained if electrons had integer wavelengths. Debye didn’t like the idea and suggested that if “something were a wave it needed a proper wave equation”. Schrodinger took this remark seriously. After a lengthy absence working on the problem, he returned to Zurich on January 9 of 1926 and eventually completed the equation. Shortly after, he opened a talk with these words, “My colleague Debye suggested that one should have a wave equation, well I have found one!”. Schrodinger then published a series of six papers in 1926 titled “Quantization as a Problem of Proper Values”.
Schrodinger’s equation incorporated a wave function where Ψ related the wave- length to momentum and frequency to energy.
The Ψ included the complex number i, which disturbed Schrodinger at first since it would cause the introduction of the imaginary component. This term was problematic because its presence implied that the wave function had a dimension which was not observable. Schrodinger had initially hoped that Ψ would represent the vibration process in the atom, and that the superposition of the waves would create a so-called wave packet (which would explain what was happening when Ψ acted like a single particle). Soon, however, Schrodinger came to a realization which he mentioned in the final part of his Quantization paper series: he realized Ψ function itself can’t be interpreted in terms of three dimensional space directly. Nevertheless, the equation more or less did what he wanted and described the particles world in a more intuitive way.
In the summer of 1926 Max Born, who was Heisenberg’s supervisor, published his work on atomic collision. Born regarded collisions as one of the key issues in understanding the atomic realm.He had struggled with the matrix mechanics approach and openly declared, ”Only Schrodinger’s formalism proved itself appropriate for this purpose. For this reason I am inclined to regard it as the most profound formulation of quantum laws”. However, Born could not make sense of Schrodinger’s claim that the Ψ function referred to an electron’s charge density. He concluded that Schrodinger’s equation did not tell us about the state of the an event, but rather the probability of a state. With this theory,Born ushered in the era of different interpretations of waves and the Schrodinger equation.
Ever since then, the physicist’s view of the world has changed in that the person making the measurement is not merely an observer but a part of the system. All of this does require a rethinking of the nature of reality. Many scientists at the time considered it a sacrifice to bring probability into their equations in exchange for the greater precision afforded by quantum mechanics.