# Shape of the container and the number of possible energy states

A question came up when studying the formula for calculating the total number of possible energy states of a particle within a container.

Why is the number of possible energy states independent of the shape of the container and merely dependent on the number of states in only 3 perpendicular container dimensions ($$x$$, $$y$$ and $$z$$), while a momentum vector can be directed at any direction within the container? Shouldn't the length of the container in that same direction as the momentum vector also determine the number of energy states in that direction?

• The number of possible energy states is infinite; why would it be dependent of anything? – Ivan Neretin Oct 27 '18 at 21:54
• Hi Johnny, can you provide more details regarding the model you’re working with, including a citation to a textbook or other reference? It is a lot easier to answer questions of this type when the model is fully laid out. Also, this question is quite similar to your last one, and I would probably recommend editing your last question than posting a new one. – a-cyclohexane-molecule Oct 28 '18 at 11:05
• @a-cyclohexane-molecule I have made an illustration but in 2D momentum space along with the question, found here: dropbox.com/s/wsomw9odrwbrsec/Question.jpg?dl=0 Regarding my last question, the question is down the list by now and I thought it would not be bumped up and noticed by others if it is edited. – JohnnyGui Oct 29 '18 at 14:17
• Note that all edits will automatically bump questions. – a-cyclohexane-molecule Oct 29 '18 at 22:23
• @a-cyclohexane-molecule So shall I put my illustration in my previous question and ignore this one for now? – JohnnyGui Oct 30 '18 at 21:40