Increasing confidence in theoretical calculations

[ergospherical]

How can one maximise one's confidence in the results of a theoretical calculation? After long and fiddly calculations I often encounter an uneasy feeling where I find it difficult to confirm whether the fruits of all that labour are actually correct. The first ports of call are always:

- dimensional consistency;
- physical reasonableness; is the behaviour unusual? are there different regimes? extreme cases?
- does the result depend on the variables I expected it to? symmetry considerations? scale invariance?
- consistency with similar problems? does the solution reduce to those of special cases?
- does the computer agree with your maths? (did you miss a minus sign on line 37...?)

Some less conclusive tests are:
- "niceness"; a short, tidy answer inspires confidence, but a long, messy answer is not necessarily incorrect.
- peer-review; ask your friend - did (s)he get the same thing?

I'm especially interested to hear about how a theoretical physicist would go about verifying his/her results before publication to a journal/competition etc.

 

[robphy]

In addition to your list, I would add...
- comparison with alternate approaches? - use another method to try to get the same result (and compare advantages and disadvantages... in particular, understand its limitations... where would your approach fail?
What was tried by others in the past? Why did those succeed or fail?)
- clear presentation? - crudely, a storyline to present to someone else who might not follow all of the details; clear definitions and terminology? good notation?
- what does it mean? Is it valuable? - does anybody care? (If not, can one make them care about it?)
- (anticipate follow up questions... what next?)

 

[gmax137]

I'm especially interested to hear about how a theoretical physicist would go about verifying his/her results before publication to a journal/competition etc.

Comparison with experiment?

 

[ergospherical]

Comparison with experiment?

Whilst true in principle, I ought to have clarified that I am only here concerned with analytical techniques (think sitting at a desk with only a pen/paper/laptop, solving a theoretical problem). In other words it's out of the question to perform an experiment, for reasons of feasibility/equipment/expense/time/etc.