How to Understand Quantum Physics

Reviewed by Grace Imson, MA

Last Updated: November 3, 2024 Fact Checked

Quantum physics (also known as quantum theory or quantum mechanics) is a branch of physics providing a description of the behaviour and interaction of matter and energy on the scale of subatomic particles, photons and certain materials at very low temperature. The quantum realm is defined as being where the "action" (or sometimes the angular momentum) of the particle is within a few orders of magnitude of a very tiny physical constant called the Planck constant.

Part 1

Part 1 of 8:

Planck Constant

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Start with learning about the physical significance of the Planck constant. In quantum mechanics, the quantum of action is the Planck constant, usually denoted as h . Likewise, for interacting subatomic particles, the quantum of angular momentum is the reduced Planck constant (the Planck constant divided by 2π) denoted by ħ and called "h-bar". The value of the Planck constant is extremely small, its units are those of angular momentum, and the notion of action is the more general mathematical concept. As the name quantum mechanics implies, certain physical quantities such as angular momentum can change only in discrete amounts, and not in a continuous ( cf. analog) way. ^{[1]
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- For example, the angular momentum of an electron bound to an atom or molecule is quantized and can only have values that are multiples of the reduced Planck constant. This quantization gives rise to electron orbitals of a series of integer primary quantum number. In contrast, the angular momentum of a nearby unbound electron is not quantized. The Planck constant also plays a role in the quantum theory of light, where the quantum of light is the photon and where matter and energy interact via the atomic electron transition or "quantum leap" of the bound electron.
- The units of the Planck constant can also be viewed as energy times time. For example, in the subject area of particle physics, the notion of virtual particles are messy particles that spontaneously appear out of the vacuum for a tiny fraction of a section and play a role in a particle interaction. The limit to the lifetime of these virtual particles is the energy (mass) of the particle times that lifetime. Quantum mechanics is a large subject area but every part of its mathematics involves the Planck constant.
Massy particles go through a classical-to-quantum transition. Even though the free electron displays some quantum properties (such as spin), as the unbound electron approaches the atom and slows down (perhaps by emitting photons), it undergoes a transition from classical to quantum behavior as its energy goes below the ionization energy. The electron is then bound to the atom and its angular momentum with respect to the atomic nucleus is restricted to quantized values of the orbitals it can occupy. The transition is sudden. One might compare this transition with that of a mechanical system that changes from displaying unstable to stable behavior or from displaying simple to chaotic behavior, or even a rocket ship slowing and going below escape velocity and entering orbit around some star or other celestial object. In contrast photons (which are massless) do not go through such a transition: photons just travel through space unchanged until they interact with other particles and then disappear. As you look into the night sky, the photons from some star traveled through light years of space unchanged then interacted with an electron in a molecule of your retina, transferred its energy and then otherwise disappeared. ^{[2]
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Part 2

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Novel Ideas

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Be across the novel ideas presented in Quantum Theory. You'll need to be familiar with these, among them being: ^{[3]
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1. The quantum realm follows rules quite different from the everyday world we experience.
2. Action (or angular momentum) is not continuous, but comes in small but discrete units.
3. The elementary particles behave both like particles and like waves.
4. The movement of a specific particle is inherently random and can only be predicted in terms of probabilities.
5. It is physically impossible to simultaneously measure both the position and the momentum of a particle beyond the accuracy allowed by the Planck constant. The more precisely one is known, the less precise the measurement of the other is.

Part 3

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Particle and wave duality

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Study the concept of particle and wave duality. This postulates that all matter exhibits both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects. ^{[4]
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- For complete knowledge of matter duality, one must have concepts of Compton effect, photoelectric effect, de Broglie wavelength, and Planck's formula for black-body radiation. All these effects and theories prove the dual nature of matter.
- There are different experiments for light set by scientists proving that light has a dual nature i.e. particle as well as wave nature (e.g., the double-slit experiment ^{[5]
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  Research source} ). In 1901, Max Planck published an analysis that succeeded in reproducing the observed spectrum of light emitted by a glowing object. To accomplish this, Planck had to make an ad hoc mathematical assumption of quantized action of the oscillators (atoms of the black body) that emit radiation. It was Einstein who later proposed that it is the electromagnetic radiation itself that is quantized into photons.

Part 4

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Uncertainty

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The uncertainty principle states that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known to arbitrarily high precision. In quantum physics, a particle is described by a wave packet, which gives rise to this phenomenon. Consider the measurement of the position of a particle. It could be anywhere. The particle's wave packet has non-zero amplitude, meaning the position is uncertain – it could be almost anywhere along the wave packet. To obtain an accurate reading of position, this wave packet must be 'compressed' as much as possible, meaning it must be made up of increasing numbers of sine waves added together. The momentum of the particle is proportional to the wave number of one of these waves, but it could be any of them. So a more precise position measurement – by adding together more waves – means the momentum measurement becomes less precise(and vice versa). ^{[6]
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Part 5

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Wave function

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Learn about wave function. A wave function or wave function is a mathematical tool in quantum mechanics that describes the quantum state of a particle or system of particles. It is commonly applied as a property of particles relating to their wave-particle duality, where it is denoted ψ (position, time) and where |ψ| ² is equal to the chance of finding the subject at a certain time and position. ^{[7]
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- For example, in an atom with a single electron, such as hydrogen or ionized helium, the wave function of the electron provides a complete description of how the electron behaves. It can be decomposed into a series of atomic orbitals which form a basis for the possible wave functions. For atoms with more than one electron (or any system with multiple particles), the underlying space is the possible configurations of all the electrons and the wave function describes the probabilities of those configurations.
- In solving homework problems involving the wave function, familiarity with complex numbers is a prerequisite. Other prerequisites include the math of linear algebra , Euler's formula from complex analysis and the bra–ket notation.

Part 6

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Schrödinger Equation

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Understand the Schrödinger equation. It is an equation that describes how the quantum state of a physical system changes in time. It is as central to quantum mechanics as Newton's laws are to classical mechanics. Solutions to the Schrödinger equation describe not only molecular, atomic and subatomic systems, but also macroscopic systems, possibly even the whole universe. ^{[8]
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- The most general form is the time-dependent Schrödinger equation which gives a description of a system evolving with time.
- For systems in a stationary state, the time-independent Schrödinger equation is sufficient. Approximate solutions to the time-independent. Schrödinger equations are commonly used to calculate the energy levels and other properties of atoms and molecules.

Part 7

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Quantum Superposition

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Quantum superposition refers to the quantum mechanical property of solutions to the Schrödinger equation. Since the Schrödinger equation is linear, any linear combination of solutions to a particular equation will also be a solution of it. This mathematical property of linear equations is known as the superposition principle. In quantum mechanics such solutions are often made to be orthogonal, such as the energy levels of an electron. By doing so the overlap energy of the states is nullified, and the expectation value of an operator (any superposition state) is the expectation value of the operator in the individual states, multiplied by the fraction of the superposition state that is "in" that state. ^{[9]
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Part 8

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Ignoring the Classical Picture

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Let go of classical notions of physics. In quantum mechanics, the path of the particle is idealized totally in a different manner and the old quantum theory is just a toy model to understand the atomic hypothesis. ^{[10]
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- In Q.M., the path of the particle is imagined as if it has gone through many paths,in classical mechanics the path of particle is determined by its trajectory but, in Q.M there are multiple paths in which the particle can travel. This truth is hidden in the double slit experiment and in which the electron behaves as wave particle duality and this idea is clearly explained by Feynman`s path integral.
- In Q.M., the normalization constant ensures the probability of finding the particle is 1.
- Completely ignore the "toy model" (Bohr's model) to understand the higher level of Q.M. The reason is simple––you can't determine the exact path of the electron in various orbital level.
- If the Q.M approaches the classical limit (i.e) h tends to zero, the Q.M results somewhat approaches the results which are nearer to classical.
- In Q.M., the classical results are obtained using the expectation value and the best example is Ehrenfest's theorem. It is derived using the operator method.

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I really want to learn Quantum Mechanics. How can I learn it by myself?

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Find the most highly recommended texts on the subject at a library or bookstore, select the ones that look best to you, and attempt to read them.

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What are eigenvalues?

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Whenever we make a measurement on an observable in a particular state, the eigenvalues are the possible results of the measurement. Having an eigenvalue implies that the observable can exist in that particular state with zero uncertainty.

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Does a single electron split into multiple pseudo-particles which create a wavelike shape and then go through double slit?

Henry Sheehy

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No. Electrons cannot split, as far as we can tell. There is an analogous statement to the one which you describe, but for waves. It's called Huygens Principle. To really understand interference, think about the electron's wavefunction as a measure of its probability. It tells you where you may find the electron. Then when you measure you collapse the wavefunction to be in one of its many possibilities, and that's where you see an electron particle.

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Solve the numerical problems of high school physics as a practice for the work required to solve the math in Quantum physics.

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Some of the prerequisites of Quantum Physics include the concepts of Classical mechanics, Hamiltonian and different properties of waves like interference, diffraction etc. Consult appropriate text books and reference books or ask your physics teacher. One should gain a strong understanding of high school physics and the prerequisites of high school physics. You will need to learn quite a bit college-level math.

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How to Understand Quantum Physics

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Planck Constant

Novel Ideas

Particle and wave duality

Uncertainty

Wave function

Schrödinger Equation

Quantum Superposition

Ignoring the Classical Picture

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