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I have a problem about the eigenvalue of the system and the eigenvalue of the part of the system.

For example,in the theory of the APW method,the space of the primitive cell is divided into muffin-tin (MT) spheres and the interstitial region (IR). In order to gain the eigenvalue and the eigenfunction of the primitive cell,we usually assume the eigenvalue [itex]E^{'}[/itex] of MT ,then determine its eigenfunction ,and then we sovle the eigenvalue [itex]E[/itex] and eigenfunction of the entire primitive cell.

Here,the eigenvalue [itex]E[/itex] of the system must belong to the the eigenvalue [itex]E^{'}[/itex] of MT (it means [itex]E \subset E^{'}[/itex],mathematically),isn't it ? Can anyone explain the physical meaning of the relationship ?

Regards,

Douasing

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# Eigenvalue of the system and the one of its part

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