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1 Introduction to Superposition
In this section, we review the concepts of classical and quantum superposition. Quantum superposition is the framework for understanding all quantum phenomena. As we do not observe quantum phenomena in our everyday lives, it may seem confusing at first. However, as unintuitive as the quantum world may appear, there are a vast number of experiments which conclusively show that the universe really does operate according to the law of quantum superposition at the smallest distances accessible today. Before going into specific details on quantum superposition, it is useful to explain how the term “superposition” is used in different contexts in both classical and quantum physics. At the end of the chapter, we present the related activities and questions. After gaining experience with quantum superposition from working through these problems, it will become more intuitive. The more experience you gain by advancing through this book, the more quantum superposition will make sense.
1.1 Classical Superposition
In classical physics, the concept of superposition is used to describe when two physical quantities are added together to make another third physical quantity that is entirely different from the original two. An example of the “superposition principle” in classical physics is clear when working with waves. Two pulses on a string which pass through each other will interfere following the principle of superposition as shown Fig. 1.1. Noise-canceling headphones use superposition by creating sound waves with the same magnitude as the incoming sound wave but completely out of phase, thereby canceling the sound wave. This destructive interference is illustrated in the second figure of Fig. 1.1.
Another common application of classical superposition is finding the total magnitude and direction of quantities such as force, electric field, magnetic field, etc. For example, to calculate the total electric force Ftotal on a charge q2 produced by other charges q1 and q3, one would sum the forces produced by each individual charge: Ftotal = F12 + F32. The challenge here is that forces are vectors, so vector addition is needed, as shown in Fig. 1.2.
1.2 Quantum Superposition
Quantum superposition is a phenomenon associated with quantum systems. Quan- tum systems include small objects such as nuclei, electrons, elementary particles, and photons, for which the wave-particle duality and other non-classical effects are observed. For example, you would normally expect that an object can have an arbitrary amount of kinetic energy ranging from 0 to infinity (∞) Joules, i.e. a baseball could be at rest or thrown at any speed. However, according to quantum mechanics, the ball’s energy is quantized, meaning it can only have certain values.
Fig. 1.3 Quantum effects associated with energy quantization are important at the atomic and subatomic distances. In this figure, the grey lines represent allowed energies. In quantum systems, the energies are quantized. As we zoom out of the quantum system to see it through a classical lens (represented by the downward arrow), the energies become more dense and appear continuous. This is the reason quantization is not noticeable in everyday objects
Fig. 1.4 A tossed coin has a 50% chance of landing on heads or tails
A specific example of energy quantization is when energies can only have integer values E = 0, 1, 2, 3, . . ., but not any numbers inbetween. This is counterintuitive, as we cannot observe it with our classical eyes. The gaps in energy are too small to be seen with the human eye and as such can be treated as continuous for classical physics. However, the gaps are more pronounced at smaller sizes, as shown in Fig. 1.3. For example the hydrogen atom is small enough that quantum effects are important, and Bohr needed to quantize the energy levels to successfully model its behavior.
One aspect of quantum superposition can be explained using a coin analogy. A coin has a 50/50 probability of landing as either heads or tails, as shown in Fig. 1.4.
