Why does the schwa (ə) sound so differently in different words? It is a one sound so doesn’t it have to be pronounced identically or alike? For example words problem (ˈprɑː.bləm orˈprɒb.ləm) and AmericA (əˈmer.ɪ.kə) has the schwa sound in the end of them but the sound is very different. In word problem ə sounds like a short e or æ but in word America it’s just a regular ɑː or ʌ.
I haven’t seen this in the other sounds. All of them are pronounced in the same way.

Question

Why does the schwa (ə) sound so differently in different words? It is a one sound so doesn’t it have to be pronounced identically or alike? For example words problem (ˈprɑː.bləm orˈprɒb.ləm) and AmericA (əˈmer.ɪ.kə) has the schwa sound in the end of them but the sound is very different. In word problem ə sounds like a short e or æ but in word America it’s just a regular ɑː or ʌ. 
I haven’t seen this in the other sounds. All of them are pronounced in the same way.

Answer

Sometines the sounds in a word or phrase are affected by the sounds next to them. This can cause moderate differences in a phoneme (sound). Stress might also be a factor.

Answer

Yeah this is an interesting example. I’d never thought about how the schwa actually sounds slightly different in each word.

They do have a different sound.

In this case, I recommend just pronouncing it without the schwa. “Prob-lm”

I recommend the same thing with words like “development”. Duh-ve-lup-mnt.

Answer

I am not an expert.

The schwa is also called "the indefinite vowel." I assume that is because it does NOT have any fixed sound.

What happens if you just ignore the sound and let your mouth do whatever feels easiest?

I think the schwa is just what happens if you connect two consonants together and don't care about the sound--the sound is not meaningful.