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Ball in a Box

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.

That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/ball-in-a-box/

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Exercise:
An elastic ball mass mO is confined in a ondimensional box width LO. It moves with vO. abcliste abc Calculate the ball's kinetic energy and determine the quantum number n for this energy level. abc Calculate the distance between two neighbouring maxima of the probability density. abcliste

Solution:
The kinetic energy is sscEkin EkF fractimesmtimesv^ resultEkP- The energy for the nth eigenstate is E_n fracn^pi^hbar^mL^ Solving for n yields n nF fracsqrttimesmtimesEktimesLpitimesnchbar resultnS The distance between two maxima of the probability density corresponds to lambda/: Delta x fraclambda_n fracpik_n fracpik_n fracpi Lnpi dxF fracLn resultdxS This is much smaller than the distance between two atoms. The probability maxima are so dense that for any realistic measurements the probability density can be ased to be constant.

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Branches	quantum physics
Tags	energy level, potential well
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Difficulty	(2, default)
Points	0 (default)
Language	(English)
Type	Calculative / Quantity
Creator	by
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