Add method to calculate excited eigenstates of a Hamiltonian

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+++ new
@@ -1,3 +1,29 @@
+#####What and Why#####
+
+Currently, we have only one eigenstate solver that diagonalizes the Hamiltonian matrix. While this works fine in general, such a diagonalization becomes not very useful for very large systems (~10k grid points), because the computational complexity scales very unfavorably.
+
+On the other hand, you often do not want to have _all_ eigenstates, but just the lowest few (after all, you want to solve the time-dependent Schroedinger equation). An example would be a state with finite, but low temperature, where you sum over a handful of eigenstates to get the thermal average.
+
+Two solvers seem useful:
+
+* Iterative Arnoldi method. That is, propagate in imaginary time to get the groundstate, then propagate again while always projecting out the groundstate to get the first excited state etc.
+* Lanczos method. Repeatedly apply the Hamiltonian to a random initial test state and solve the eigenvalue problem in the resulting Krylov subspace. There are various issues about usability (a random starting vector may not give all relevant eigenstates), but in general the method seems fast and easy enough to implement.
+
+The suggestion would be to implement the Lanczos method unless there are severe obstacles.
+
+
+#####Acceptance criteria#####
+
+*  Implement a method to get some approximate eigenstates and -energies for a given problem
+** squeeze the solver into the EigenstatePrimitive interface, i.e., that it can be used like any other solver.
+* Add a demo that highlights the usage and ideally potential pitfalls
+
+----
+
+Old content
+
+
+
 #####What and Why#####

 One technique for getting the lowest few eigenstates of a Hamiltonian is repeated relaxation.

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@@ -1,29 +1,3 @@
-#####What and Why#####
-
-Currently, we have only one eigenstate solver that diagonalizes the Hamiltonian matrix. While this works fine in general, such a diagonalization becomes not very useful for very large systems (~10k grid points), because the computational complexity scales very unfavorably.
-
-On the other hand, you often do not want to have _all_ eigenstates, but just the lowest few (after all, you want to solve the time-dependent Schroedinger equation). An example would be a state with finite, but low temperature, where you sum over a handful of eigenstates to get the thermal average.
-
-Two solvers seem useful:
-
-* Iterative Arnoldi method. That is, propagate in imaginary time to get the groundstate, then propagate again while always projecting out the groundstate to get the first excited state etc.
-* Lanczos method. Repeatedly apply the Hamiltonian to a random initial test state and solve the eigenvalue problem in the resulting Krylov subspace. There are various issues about usability (a random starting vector may not give all relevant eigenstates), but in general the method seems fast and easy enough to implement.
-
-The suggestion would be to implement the Lanczos method unless there are severe obstacles.
-
-
-#####Acceptance criteria#####
-
-*  Implement a method to get some approximate eigenstates and -energies for a given problem
-** squeeze the solver into the EigenstatePrimitive interface, i.e., that it can be used like any other solver.
-* Add a demo that highlights the usage and ideally potential pitfalls
-
-----
-
-Old content
-
-
-
 #####What and Why#####

 One technique for getting the lowest few eigenstates of a Hamiltonian is repeated relaxation.
@@ -40,5 +14,5 @@

 #####Acceptance criteria#####

-* There is an EigenstatePrimitive implementation that implements this scheme.
+* There is some implementation of this scheme (factory/*?)
 * There is a highlighted demo that demonstrates the use of this scheme.

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 * There is some implementation of this scheme (factory/*?)
 * There is a highlighted demo that demonstrates the use of this scheme.
+
+
+----
+
+Note: Originally tried Lanczos algorithm, but doing this turned out to be pretty tricky, so I deferred this to [#203]

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@@ -21,3 +21,5 @@
 ----

 Note: Originally tried Lanczos algorithm, but doing this turned out to be pretty tricky, so I deferred this to [#203]
+
+Instead I went for repeated relaxation including the MolVibration/H3+ demo