Quantum mechanics is a difficult subject to teach due to its counterintuitive nature. As the subject is now offered by advanced secondary schools, educators have applied scientific methodology to the process of teaching quantum mechanics, in order to identify common misconceptions and ways of improving students' understanding.

Common learning difficulties

Students' misconceptions range from fully

classical physics Classical physics refers to physics theories that are non-quantum or both non-quantum and non-relativistic, depending on the context. In historical discussions, ''classical physics'' refers to pre-1900 physics, while '' modern physics'' refers to ...

thinking, mixed models, to quasi-quantum ideas. For example, if the concept that quantum mechanics does not describe a path for

electrons The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

photons A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that ...

is misunderstood, students may believe that they follow specific trajectories (classical), or sinusoidal paths (mixes), or are simultaneously wave and particles (quasi-quantum: "in which students understand that quantum objects can behave as both particles and waves, but still have difficulty describing events in a nondeterministic way"). Among the concepts most often misunderstood are: * the postulates of quantum mechanics provide no description for the trajectories for electrons or photons, * amplitude of a

wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...

is not a measure of

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

, * most

bound states A bound state is a composite of two or more fundamental building blocks, such as particles, atoms, or bodies, that behaves as a single object and in which energy is required to split them. In quantum physics, a bound state is a quantum state of a ...

have no corresponding classical

orbits In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificia ...

, * in practice, quantum mechanics gives probabilisitic rather than

deterministic Determinism is the metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping mo ...

results, * intrinsic

uncertainty Uncertainty or incertitude refers to situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown, and is particularly relevant for decision ...

rather than

measurement error Observational error (or measurement error) is the difference between a measured value of a quantity and its unknown true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. Such errors are inherent in the measurement pr ...

. Issues also arise from misunderstanding classical concepts related to quantum concepts, such as the difference between light energy and light intensity.

Teaching strategies

Mathematics

Quantum mechanics can be taught with a focus on different interpretations, different models, or via mathematical techniques. Studies have shown that focus on non-mathematical concepts can lead to adequate understanding.

Digital and multi-media

Despite the fundamental impossibility of directly viewing quantum states, multimedia visualizations are an important tool in education. Interactive media provides an alternative experience beyond everyday personal experience as a tool for understanding quantum mechanics. Among the multimedia sites that have been studied with positive results ar
QuVis
an

History and philosophy of science as educational guides

In introducing history as part of the process of teaching quantum mechanics sets up a potential conflict of goals: accurate history or pedagogical clarity. Studies have shown that teaching through history helps students recognize that the counterintuitive issues are fundamental rather than simply something they don't understand. Specifically discussing the historical debates on quantum concepts drives home the idea the quantum differs from classical. Discussing the

philosophy of science Philosophy of science is the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science, the reliability of scientific theories, ...

introduces the idea that language derived from everyday experience limits our ability to describe quantum phenomena.

Directly discussing the meanings of words

Mohan analyzes two widely used representative quantum mechanics textbooks against the learning challenges reported by Krijtenburg-Lewerissa and others. Both texts adopt language ('waves' and 'particles') familiar to students in other contexts without directly exploring the significant shifts in meaning required by quantum mechanics. Mohan attributes some of the learning challenges to this unexplored application of inappropriate language.

Teaching for quantum computing

N. David Mermin reports that an unconventional strategy based on abstract but simple math concepts is sufficient to teach quantum mechanics to students interested in

quantum computing A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of wave-particle duality, both particles and waves, and quantum computing takes advantage of this behavior using s ...

application rather than physics. Many of the issues that confound students of physics to not apply to this case and the mathematical background of quantum computing resembles the background already taught in

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

. Mermin develops notation and operations with classical bits then introduces quantum bits as superpositions of two classical states. He never needs to discuss even the

Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

, which he suggests is important for quantum computer hardware but not software.

Teaching based on quantum optics

Philipp Blitzenbauer engages students through simple but intrinsically quantum single-photon experiments. The approach avoids the ambiguous classical vs quantum character of photons in optical interference experiments like the double slit. Students exposed to quantum mechanics in this way avoid developing misconceptions apparent among students in the control group.

Notes

References

{{reflist Quantum mechanics Pedagogy