From Diracvideo

[edit] How to Pronounce (and Spell) Schrödinger

Schrödinger is German surname, so is normally spelled with an "ö". This is transliterated to English as "oe", so Schroedinger is also considered correct, especially in situations where the writer is limited to English (ahem, ASCII).

The "ö" vowel doesn't really exist in English, and attempting to teach it in a web site seems like a mistake. If you know the vowel, use it. Otherwise, use the English pronunciation of the name, which pronounces the vowel like the 'o' in code.

The "inger" is as in singer, not finger, and definitely not like "ger" in German. If you are a native English speaker, and you think "singer" and "finger" sound the same, you're doing it wrong.