18.3 Electron Double Slit Experiment and Quantum Mechanics

The Electron Double-Slit Experiment

In the classic double-slit experiment, a beam of electrons is fired at a barrier containing two narrow slits. A detector screen records where each electron lands.

Key Observations

1. Interference pattern forms: When both slits are open and no detector monitors which slit each electron passes through, an interference (diffraction) pattern of alternating bright and dark fringes builds up on the screen — exactly like a wave.
2. Single electrons still interfere: Even when electrons are fired one at a time, the same interference pattern gradually emerges. This means each electron interferes with itself, passing through both slits simultaneously as a probability wave.
3. Observation destroys the pattern: If a detector is placed at the slits to determine which slit the electron passes through, the interference pattern disappears and is replaced by two bright bands — the electrons now behave like classical particles.

Evidence for Wave Nature of Particles

The interference pattern is direct experimental evidence that electrons (and all matter) possess a wave nature. The wavelength associated with a moving electron is given by the de Broglie relation:

$\lambda =\frac{h}{p}=\frac{h}{mv}$

where:

• $h=6.63\times 10^{-34}\text{ J s}$ is Planck's constant
• $m$ is the electron mass
• $v$ is the electron's speed
• $p=mv$ is the electron's momentum

Inverse relationship: If the electron's velocity is doubled, its de Broglie wavelength is halved.

The fringe spacing in the electron double-slit experiment matches the prediction from this wavelength, confirming the wave nature of matter.

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Wave Function and Probability

Quantum mechanics describes the electron using a wave function $\psi$. The physical meaning is:

$\text{Probability density}=|\psi {|}^2$

This gives the probability of finding the electron at a particular location when a measurement is made. The wave function does not describe a definite path — the electron exists in a superposition of all possible paths until it is observed.

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Interpretations of Quantum Mechanics

1. Copenhagen Interpretation

Proposed by Niels Bohr and Werner Heisenberg, this is the most widely taught interpretation:

• The wave function $\psi$ represents the complete description of the quantum state.
• $|\psi {|}^2$ gives the probability density of finding the particle at a given position.
• Before measurement, the electron has no definite position — it exists in superposition.
• Upon measurement, the wave function collapses instantaneously to a definite state.
• In the double-slit experiment: the electron's wave function passes through both slits and interferes with itself. When a detector is used to identify which slit, the wave function collapses and the interference pattern is destroyed.

2. Many-Worlds Interpretation

Proposed by Hugh Everett III (1957):

• There is no wave function collapse. Instead, every quantum measurement causes the universe to branch into multiple parallel universes.
• In one branch the electron goes through slit 1; in another branch it goes through slit 2.
• All outcomes occur — in different branches of reality.
• The interference pattern arises from the interaction between branches.
• This interpretation avoids the need for a special role of the observer.

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Principle of Complementarity

Niels Bohr's Principle of Complementarity states:

• When we observe which slit the electron passes through → particle behaviour (no interference).
• When we do not observe the path → wave behaviour (interference pattern).

This is not a limitation of our instruments — it is a fundamental feature of nature.

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Summary Table