Where can you find the quantities of each amino acid of a particular protein or food?
There's a fantastic database available from the United States Department of Agriculture that includes almost 9,000 common foods, including their nutritional information. This database is searchable and available from the USDA Agricultural Research Service. Here is a link for the online searchable database. 

Within the database you are able to search for a number of parameters; including, food composition, water content, individual amino acid content, fatty acid and total fat content, vitamins, minerals, phytonutrients, and more! One of the nice things is that you can ask it to rank the foods in order of nutrient composition. For example, ranking all the foods in the database in order of protein content or a specific amino acid (or whatever else you're interested in).

It's a great database, especially for researchers that need a database of trusted nutrient data.

 

Within the database you can search by nutrient or by food, whichever you are curious about. For example, as you mention in the question, I entered potato and in the second screen shot below you can see the listing of all the nutrients in the potato. These are listed as % weight per 100g of potatoes - with or without the skin.



To get to the amino acid content breakdown, click on Full Report (All Nutrients) at the top.