Learn basics of Quantum Physics in 6 Steps

  1. Planck constant

The modern physics of quantum mechanics was born in 1900 when Max Planck after many unsuccessful attempts in an "act of despair" introduced a universal smallest quantum of action  h=6.626×10−34Js=4.12×10−15eVs named Planck's constant in a theoretical justification of the spectrum of radiating bodies observed in experiments, based on statistics of packets of energy of size hν with ν frequency.

Planck describes this monumental moment in the history of science in his 1918 Nobel Lecture as follows:

• For many years, such an aim for me was to find the solution to the problem of the distribution of energy in the normal spectrum of radiating heat.
• Nevertheless, the result meant no more than a preparatory step towards the initial onslaught on the particular problem which now towered with all its fearsome height even steeper before me. The first attempt upon it went wrong…
• So there was nothing left for me but to tackle the problem from the opposite side, that of thermodynamics, in which field I felt, moreover, more confident. 
• Since the whole problem concerned a universal law of Nature, and since at that time, as still today, I held the unshakeable opinion that the simpler the presentation of a particular law of Nature, the more general it is… 
• For this reason, I busied myself, from then on, that is, from the day of its establishment, with the task of elucidating a true physical character for the formula, and this problem led me automatically to a consideration of the connection between entropy and probability, that is, Boltzmann's trend of ideas; until after some weeks of the most strenuous work of my life, light came into the darkness, and a new undreamed-of perspective opened up before me.

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2. Uncertainty

Classical physics was on loose footing with problems of wave/particle duality, but was caught completely off-guard with the discovery of the uncertainty principle.

The uncertainty principle also called the Heisenberg Uncertainty Principle, or Indeterminacy Principle, articulated (1927) by the German physicist Werner Heisenberg, that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory. The very concepts of exact position and exact velocity together, in fact, have no meaning in nature.

But why can't we detect particles position or moment with a big precision? Well it's mostly because of the way we detect particles. Long story short, we detect a particle by shooting a photon at it (a particle of light). However, a photon also has some momentum and as strange as it sounds you can simply "knock" a particle away with a photon. Also, if you want to find out the position of a particle with a high precision, you must use a high frequency light wave (a high energy photon, where the energy of a photon E is given by E=hf, where h- Planck constant and f- frequency) which naturally has a bigger momentum, which causes a particle to be knocked away at a high velocity. This is exactly what causes the uncertainty in the momentum.

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3. Particle and wave duality

  In 1905, Einstein had suggested that light has duel character. In analogy with the behaviour of light, de Broglie suggested that all material particles should also show dual behaviour. In 1924, de Broglie suggested that electron has duel character. This suggestion recieved first experimental support from Davission and German in 1927. They found that the impact of electron on crystal resulted in the production of diffraction pattern which were similar to those given by x-rays under similar condition. Since x-rays posses wave character, electrons must also have wave character associated with them. Thus this experiment gave direct evidence for wave character of electrons, nutrons, protons, hydrogen atom, C₆₀ (fullerene) etc.

The similarity of these two patterns shows that electrons can behave like X-rays and display wave properties.

In Bohr theory, electron is treated as a particle. But according to de-Broglie, electron has a duel character; both as a material particle and as a material particle and as a wave. He derived an expression for calculating the wave length 'λ' of a particle of mass 'm' moving with velocity 'v'.

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4. Schrödinger Wave function

    Scientists of early 20^th century tried to explain the behaviour of atom on the basis of dual nature of matter and uncertainty principle. They had to develop a new view of matter and energy to accurately describe how atoms behaved. This attempt is called Wave Mechanics or Quantum Mechanics. This theory describes matter as, acting both as a particle and as a wave. In case of visible objects in every day life the wave length is too small to be apparent. Wave like nature becomes important in microscopic particles such as electrons. Due to the wave nature of electrons they exist as a fizzy cloud of negative charge around the nucleus, instead of as a particle located at a single point.

In 1926, Erwin Schrodinger suggested an equation to describe the movement of electron in an atom. The equation is known as Schrodinger Wave Equation (SWE) and it is written as:

are the second differential coefficient of ψ with respect to x,y and z, E is the total energy of electron, 'm' is the mass of electron and ψ (psi) is the wave function.

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5. Quantum superposition

Superposition is a principle of quantum theory that describes a challenging concept about the nature and behavior of matter and forces at the sub-atomic level. The principle of superposition claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously, as long as we don't look to check. It is the measurement itself that causes the object to be limited to a single possibility.

In 1935, Erwin Schrodinger proposed an analogy to show how superposition would operate in the every day world: the somewhat cruel analogy of Schrodinger's cat. Here's Schrödinger's (theoretical) experiment: We place a living cat into a steel chamber, along with a device containing a vial of hydrocyanic acid. There is, in the chamber, a very small amount of a radioactive substance. If even a single atom of the substance decays during the test period, a relay mechanism will trip a hammer, which will, in turn, break the vial and kill the cat. The observer cannot know whether or not an atom of the substance has decayed, and consequently, cannot know whether the vial has been broken, the hydrocyanic acid released, and the cat killed. Since we cannot know, the cat is both dead and alive according to quantum law, in a superposition of states. It is only when we break open the box and learn the condition of the cat that the superposition is lost, and the cat becomes one or the other (dead or alive). This situation is sometimes called quantum indeterminacy or the observer's paradox: the observation or measurement itself affects an outcome, so that the outcome as such does not exist unless the measurement is made. (That is, there is no single outcome unless it is observed.)

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6. Ignoring the classical picture

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