1st order Pertubation energy and wavefunction

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SUMMARY

The discussion centers on the first order perturbation theory in quantum mechanics, specifically regarding the correction of perturbed energy and wavefunctions. The first order correction to the energy is expressed as ⟨ψn0|H'|ψn0⟩, where ψn0 represents the solution of the unperturbed Hamiltonian. It is established that ψn0 must be a specific eigenstate of the Hamiltonian rather than a superposition of eigenstates. The correction is calculated for a particular eigenvector, confirming that superpositions do not apply in this context.

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luxiaolei
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Hi all,

I must misunderstood somewhere, couldn't figure out the following, any helps will be greatly appreciated.

The first order correction of the pertubated energy is:

\leftψ<sub>n</sub><sup>0</sup>\langle H'\rightψ<sub>n</sub><sup>0</sup>\rangle

Where:
ψn0
Is the solution of the unpertubated Hamiltonian.

My question is can ψn0 be the general solution to the Hamiltonian or has to be a specified state vector?

i.e.,

ψn0= aψ10+bψ20

Or has to be:

ψn0=ψ10

If it can be the superposition of the eigenstates, then how to construct the first order wave function?
Thanks in advance:)
 
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The correction is calculated for a particular eigenvector of the Hamiltonian and not for a superposition of several eigenvectors.
 
dextercioby said:
The correction is calculated for a particular eigenvector of the Hamiltonian and not for a superposition of several eigenvectors.

Thank you so much!
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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