Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
For a single-particle Hamiltonian periodic under lattice translations, eigenstates can be chosen as a plane-wave phase times a lattice-periodic function and labeled by crystal momentum modulo reciprocal-lattice vectors.
wp-physics-bloch-theoremtong-solid-state-physicsmit-theory-of-solidsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
For a single-particle Hamiltonian invariant under Bravais-lattice translations, simultaneous diagonalization of the commuting translation operators allows energy eigenstates to be chosen in Bloch form. Degeneracies do not invalidate the existence statement.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-physics-bloch-theoremtong-solid-state-physicsmit-theory-of-solidsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Under lattice periodicity, eigenstates can be chosen to transform by lattice-translation characters and therefore have Bloch form.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-physics-bloch-theoremtong-solid-state-physicsmit-theory-of-solids