en.wikipedia.org/wiki/Quasiparticle
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Any system, no matter how complicated, has a ground state along with an infinite series of higher-energy excited states.
As written, this is too general. Some quantum systems, such as a free particle, have a continuous energy spectrum rather than a discrete ladder of excited states, and the lowest-energy plane-wave state is not a normalizable ground state.
Full reasoning
This sentence overstates a property that is not true for all quantum systems.
A standard counterexample is the free particle:
- MIT OpenCourseWare notes that for a free particle, "there is no restriction on the possible energies" and the energy "can be any positive number," i.e. the spectrum is continuous, not a discrete "infinite series" of excited states.
- MIT's quantum-physics lecture transcript also explains that free-particle plane-wave eigenfunctions are not normalizable on the real line. That means the would-be lowest-energy state at zero momentum is not a normalizable physical state in the ordinary sense.
So the universal claim is incorrect. Many bound systems do have a ground state plus discrete excited levels, but not every system does. Some systems have continuous spectra, and some do not have a normalizable ground state.
2 sources
- Introduction to Quantum Mechanics | MIT OpenCourseWare
For a free particle there is no restriction on the possible energies, En can be any positive number.
- MITOCW transcript: The wave for a free particle
Assuming this is on the real line, which is what we mean by saying it's a free particle, there's no constant you can multiply that by to make it normalizable. This is not a normalizable function.