I am going to apply for a postdoc position and one of the required documents is
letter of interest.
Is it the same with research statement?
The requested documents are cv, list of publications and thesis and recommendation letter.
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Consider the list of application materials: CV, list of publications and your thesis give more-or-less objective information. Recommendation letter is an opportunity for someone else to speak of you.
What is missing is the information about why you want the position and are a good fit for it. You should include this information in the letter of interest.
I am more familiar with terms "cover letter" and "letter of motivation" and there might be subtle cultural or terminological issues at play concerning what precisely should and should not be included, so you should search for country-specific information using the correct language-specific queries. Also, the university website might have information for applicants, which you should read.
Is a letter you write which defines your interests. It might be written by yourself. The objective of a letter of interest is to see if the vacancy suits with your interest.
Why is anybody will require it? Because people works with more effort when you are interested on a theme. Universities, Companies, etc. will need it to check if your personal insterests match their interests. If they match, everybody will be happy.
"A letter of interest is a great way to get your foot in the door with a company you are interested in. Read below for advice on how to write a letter of interest, as well as sample letters of interest for a variety of circumstances." Source