What is a quantum object?
A quantum object is a very small thing, like a photon (a tiny packet of light) or an electron. It is not a tiny ball and not a water wave. It is something new.
- When we detect it, it is always found in one place, as one dot. That is particle-like.
- When it travels, it spreads out and can interfere like a wave. That is wave-like.
- Where a single one lands is random. Only the pattern of many is predictable.
The double-slit experiment, one particle at a time
Shine very weak light at two narrow slits, so weak that only one photon is in the lab at a time. A sensitive screen records each photon as one dot.
- The first dots look random.
- After thousands of dots, bright and dark stripes (an interference pattern) appear.
- Close one slit and the stripes disappear.
So each single photon is affected by both slits. The same happens with electrons, atoms and even big molecules. An interferometer (a device that splits a beam into two paths and joins them again) shows the same thing with single photons.
Try it
In the 3D lab, press "Send 1" ten times. Can you guess where the next dot will land? Then press "+200" several times and watch stripes grow.
Probability waves and the wave function
Physicists describe a quantum object with a wave function, written ψ (psi). It is not a wave of water or air. It is a wave of chances.
Rule (Born rule): the chance of finding the particle at a place is proportional to |ψ|², the square of the wave's size there.
At a dark stripe, the waves from the two slits cancel, so |ψ|² = 0 and no dot ever lands. At a bright stripe they add up, so dots land often.
Superposition and measurement
Superposition means a quantum object can be in a mix of possibilities at once, such as "path A and path B", until it is measured.
Measurement gives one definite answer. After it, the superposition is gone (we say the state "collapses").
- Which-path information: if any device could tell which slit was used, the stripes vanish. It does not matter if anyone reads it.
- Quantum eraser: if that path information is erased again in the right way, stripes can come back in the sorted data.
- Decoherence: big objects bump into air and light all the time. This leaks path information to the surroundings, so we never see a cat or a cricket ball in superposition.
- Entanglement and non-locality: two particles can share one joint state. Measuring one instantly fixes what the other will show, even far away, but this cannot send a message faster than light.
Heisenberg uncertainty relation
You cannot know both the exact position and the exact momentum of a quantum object at the same time. In symbols: Δx · Δp ≥ h / 4π, where h = 6.63 × 10⁻³⁴ J s.
Make the slit narrower (smaller Δx) and the particles spread out more after it (bigger Δp). This is not because our tools are bad. It is how nature is.
Quantum technology: qubits, computers and cryptography
A normal bit is 0 or 1. A qubit can be in a superposition of 0 and 1. Measuring it gives 0 or 1 with set chances.
- Quantum computers use many qubits in superposition and entanglement to solve some problems (like simulating molecules) much faster.
- Quantum cryptography sends a secret key using single photons. A spy who measures them disturbs them, so the spy is detected.
Key formulas and definitions
- P(x) ∝ |ψ(x)|² (Born rule: chance of finding the particle)
- λ = h / p = h / (m v) (de Broglie wavelength)
- E = h f (energy of one photon)
- Δx · Δp ≥ h / 4π (uncertainty relation)
- fringe spacing Δy = λ L / d
- h = 6.63 × 10⁻³⁴ J s
Worked examples
1. Find the energy of one photon of green light, f = 6.0 × 10¹⁴ Hz.
E = h f = 6.63 × 10⁻³⁴ × 6.0 × 10¹⁴ = 3.98 × 10⁻¹⁹ J (about 2.5 eV).
2. An electron (m = 9.11 × 10⁻³¹ kg) moves at 2.0 × 10⁶ m/s. Find its de Broglie wavelength.
p = m v = 9.11 × 10⁻³¹ × 2.0 × 10⁶ = 1.82 × 10⁻²⁴ kg m/s. λ = h / p = 6.63 × 10⁻³⁴ / 1.82 × 10⁻²⁴ = 3.6 × 10⁻¹⁰ m = 0.36 nm, about the size of an atom.
3. Electrons with λ = 0.36 nm pass two slits d = 1.0 μm apart. The screen is L = 1.0 m away. Find the fringe spacing.
Δy = λ L / d = 0.36 × 10⁻⁹ × 1.0 / 1.0 × 10⁻⁶ = 3.6 × 10⁻⁴ m = 0.36 mm.
4. An electron is known to be inside a region Δx = 1.0 × 10⁻¹⁰ m. Find the smallest uncertainty in its momentum.
Δp ≥ h / (4π Δx) = 6.63 × 10⁻³⁴ / (12.57 × 1.0 × 10⁻¹⁰) = 5.3 × 10⁻²⁵ kg m/s.
5. At a point on the screen, the wave from slit 1 has size 1 and from slit 2 has size 1. Compare the chance there when the waves are in step and when they are opposite.
In step: ψ = 1 + 1 = 2, |ψ|² = 4. Opposite: ψ = 1 − 1 = 0, |ψ|² = 0. So bright stripe (4 times one slit alone) versus dark stripe (no dots).
6. A qubit has a 36% chance of giving 1. It is measured 500 times (fresh each time). About how many 1s do you expect?
0.36 × 500 = 180 ones (and about 320 zeros). Each single result is random; only the count is predictable.
Common mistakes
- Thinking the stripes come from many photons bumping into each other. They appear even when photons go one at a time.
- Thinking the wave function is a real water-like wave you can see. It is a wave of probability; we only ever see dots.
- Saying "measurement needs a human watching". Any interaction that records the path (a detector, air molecules) is enough.
- Thinking uncertainty is only due to poor instruments. It is a basic property of nature: Δx · Δp ≥ h/4π always.