به انگلیسی

A trapped wave can only sing some notes

علوم · فیزیک کوانتومی و مدرن · سن ۱۹ تا ۲۰ سال

نام ______________________ تاریخ ____________

In an infinite square well, the n=2 energy is four times the ground-state energy.
دور یکی دایره کشیدن: درست نادرست
Why does an infinite square well have discrete allowed energies?
- An extra rule excludes selected energies
- The wall conditions select fitting waves
- Friction selects the slowest wave
How many nodes lie strictly between the walls for the n=3 infinite-well wavefunction?
- 0
- 2
- 3
The width of an infinite square well is halved while particle mass stays fixed. What happens to its ground-state energy?
- It falls to one half
- It stays at its old value
- It rises to four times
For an electron in an infinite square well, use E_n=0.376 n²/L² eV, with L measured in nm. For L=2 nm, what is E2 in eV? Treat 0.376 as exact for this calculation.
پاسخ: ______________
An infinite-well state is a superposition containing only n=1 and n=2, with both present. What can one energy measurement return?
- Either E1 or E2
- Their midpoint
- Any value from E1 to E2
An infinite-well particle has E1=0.5 eV. It emits one photon carrying all the energy lost in a transition from n=2 to n=1. What is the photon energy in eV?
پاسخ: ______________
For the n=2 infinite-well state, the probability density is nonzero at the centre of the well.
دور یکی دایره کشیدن: درست نادرست

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درست · Substituting n=2 into E_n=n²E1 gives E2=4E1.
The wall conditions select fitting waves · A nonzero wave must vanish at both walls. This requires kL=nπ, selecting discrete wave numbers and energies.
2 · State n has n-1 interior nodes. For n=3, there are two, at L/3 and 2L/3.
It rises to four times · Energy varies as 1/L². Replacing L by L/2 multiplies the energy by four.
0.376 · Here n²=4 and L²=4, so E2=0.376×4/4=0.376 eV.
Either E1 or E2 · The two components have energies E1 and E2. One energy measurement returns one of those levels, not an intermediate value.
1.5 · E2=4×0.5=2.0 eV. The photon carries 2.0-0.5=1.5 eV.
نادرست · The centre is a node of the n=2 wavefunction. There ψ=0, so the probability density |ψ|² is also zero.