---
title: "Classical versus quantum mechanics"
subject: "Electrical Engineering Material"
chapter: 1
key: "semester_3/electrical_engineering_material:classical-vs-quantum-mechanics"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/classical-vs-quantum-mechanics
site: BCT Engineering
---

# Classical versus quantum mechanics

Electrical Engineering Material · Chapter 1: Theory of Metals

- Asked in: 2078 Kartik, 4 marks; 2074 Asoj, 8 marks (asked 2 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/classical-vs-quantum-mechanics
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-1

## Question

Explain the importance of quantum mechanics. Differentiate between classical and quantum mechanics with suitable examples.

## Short answer

Quantum mechanics is essential for atomic-scale phenomena like energy bands, tunneling and quantized spectra. Classical mechanics uses deterministic trajectories with continuous energy; quantum mechanics is probabilistic, uses wave functions, imposes energy quantization, limits simultaneous position–momentum knowledge (ΔxΔp ≥ ℏ), and reveals wave–particle duality.

## Answer

**Quantum mechanics** is the branch of physics that describes the behaviour of very small particles such as electrons, atoms and photons, using wave functions and probabilities instead of exact paths.

#### Importance of quantum mechanics
Classical mechanics works for large objects but fails at atomic scale. It could not explain:
- black-body radiation, the photoelectric effect and the Compton effect;
- the stability of atoms and their sharp spectral lines;
- the specific heat and electrical conductivity of metals.

Quantum mechanics explains all of these. For electrical engineering materials it is essential because it explains:
- **energy bands** and why some solids are conductors, others semiconductors or insulators;
- **effective mass**, holes and carrier concentration in semiconductors;
- **tunneling**, used in tunnel diodes, flash memory and the STM;
- the operation of lasers, LEDs, solar cells, transistors and superconductors.

#### Classical versus quantum mechanics

| Point | Classical mechanics | Quantum mechanics |
|---|---|---|
| Applies to | Large (macroscopic) bodies | Atomic and sub-atomic particles |
| Basic law | Newton's laws, $F = ma$ | Schrödinger equation |
| State described by | Exact position and momentum | Wave function $\psi$ |
| Prediction | Deterministic (exact) | Probabilistic, $|\psi|^2$ |
| Energy | Continuous | Quantized for bound particles |
| Position and momentum | Both known exactly together | Limited by $\Delta x\,\Delta p \ge \hbar$ |
| Particle vs wave | Particles and waves are separate | Wave–particle duality |
| Barriers | Particle with $E < V_0$ is always reflected | Particle can tunnel through |

#### Examples
- **Ball in a box vs electron in a well:** a ball in a box can have any speed, even zero. An electron in a 0.1 nm well can only have $E_n = n^2(37.7\text{ eV})$ and can never be at rest.
- **Barrier:** a car that cannot climb a hill never appears on the other side, but an electron with 7 eV can pass through a 10 eV, 3 nm oxide layer between copper wires with a small probability.
- **Wavelength:** a 50 g golf ball at 20 m/s has $\lambda = 6.6\times10^{-34}$ m, far too small to observe, so classical mechanics is enough; an electron accelerated through 100 V has $\lambda = 0.123$ nm, comparable to atomic spacing, so its wave nature (electron diffraction) is clearly seen.

Classical mechanics is a limiting case of quantum mechanics for large masses and large quantum numbers (correspondence principle).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How do the two theories differ in their predictions?
   A. Classical is probabilistic; quantum is deterministic
   B. Both are deterministic
   C. Classical is deterministic; quantum is probabilistic via |psi|^2
   D. Both are probabilistic
   Answer: C. Classical mechanics gives exact results, quantum mechanics gives probabilities from |psi|^2. (Key point: Prediction type)

2. How is energy of a bound particle treated?
   A. Quantized in quantum mechanics, continuous in classical
   B. Continuous in both
   C. Quantized in classical, continuous in quantum
   D. Always zero
   Answer: A. Bound particles have discrete energies in quantum mechanics, e.g. E_n = n^2 (37.7 eV) in a 0.1 nm well. (Key point: Energy)

3. A particle with E < V0 meets a barrier. What happens?
   A. Classical: tunnels; quantum: reflected
   B. Classical: always reflected; quantum: can tunnel through
   C. Both always reflect
   D. Both always transmit
   Answer: B. Classically the particle cannot cross, but quantum waves penetrate and can emerge on the other side. (Key point: Barrier behaviour)

4. Why is wave nature observable for a 100 V electron but not a golf ball?
   A. The golf ball has no wavelength
   B. Electrons are charged
   C. The electron wavelength (0.123 nm) is comparable to atomic spacing, the golf ball's (6.6e-34 m) is far too small
   D. The golf ball is too slow to have momentum
   Answer: C. de Broglie wavelength lambda = h/p is detectable only when it is comparable to atomic dimensions. (Key point: Wave nature)

## Related in Electrical Engineering Material

- [Quantum mechanics and golf ball wavelength](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Agolf-ball-de-broglie-wavelength) — Electrical Engineering Material, chapter 1