Particles as field quanta

Science · Quantum & Modern Physics · ages 23-24

Name ______________________ Date ____________

An oscillator has ħω = 0.20 eV. What is its ground state energy in eV? (Ground state means n = 0 in E_n = (n + 1/2) ħω.)
Answer: ______________
A quantum harmonic oscillator has energy levels E_n = (n + 1/2) ħω, with n = 0, 1, 2, ... What does the number n actually count?
- How many identical packets of energy ħω have been added above the ground state
- How many particles are trapped inside the oscillator
- How many times the oscillator has swung back and forth
- The spin of the oscillator
An oscillator has levels E of n = (n + 1 over 2) hw. What does n count?
- How many times it has swung back and forth
- How many identical packets of hw sit above ground
- The spin carried by the oscillator
What is a photon in the language of field modes?
- One quantum in a field mode
- A particle trapped inside an oscillator
- Half of a ground state
Why can the energy of a field mode be read as a count of particles, rather than just a number of joules?
- Because the mode's levels are evenly spaced by ħω, so its quantum number counts identical lumps of energy
- Because particles always carry exactly one joule each
- Because the field's energy can take any value at all
- Because the ground state has zero energy
What does a creation operator do to a mode?
- Raises n by one, adding a particle
- Lowers the energy to zero
- Measures the exact position
For hw = 0.50 eV, what is the energy of level n = 2 in eV?
Answer: ______________
For an oscillator with ħω = 0.50 eV, what is the energy of the n = 2 level in eV?
Answer: ______________
Why is exchange symmetry automatic in this picture?
- New fields are built for each particle
- States are built by creators, storing counts not labels
- Particles are painted with ID numbers
Rae claims particle number can never change. What is wrong?
- Ground energy is nonzero
- Creators exist only on paper
- Creation and annihilation change the count

Answer key

For grown-ups. Fold this page away before handing over the rest.

Particles as field quanta W1-mt_BJyZWQA5cb-s1

0.1 · Even with zero quanta added, the oscillator keeps half a quantum of energy. That zero point energy is the floor the particle count is measured from.
How many identical packets of energy ħω have been added above the ground state · Each step up the ladder adds exactly one quantum of energy ħω, so the quantum number n reads like an occupation count. This is the trick that later lets us read field modes as counts of particles.
How many identical packets of hw sit above ground · Each step up adds one quantum of hw above the ground state.
One quantum in a field mode · Each mode is an oscillator and its count is the photon number.
Because the mode's levels are evenly spaced by ħω, so its quantum number counts identical lumps of energy · Equal spacing is the key. Each jump costs the same ħω, so saying 'the mode is at level n' is the same as saying 'there are n quanta', and those quanta are what we call particles.
Raises n by one, adding a particle · Creators add one quantum to the occupation count.
1.25 · 2.5 times 0.50 is 1.25: ground plus two quanta.
1.25 · Level n = 2 carries two added quanta on top of the half-quantum ground state: 0.25 eV + 2 x 0.50 eV = 1.25 eV.
States are built by creators, storing counts not labels · Only occupation numbers are stored, so swapping changes nothing.
Creation and annihilation change the count · Field processes add or remove quanta freely.