die Erwartung
expectation
An idea, hope, or assumption about what will happen in the future or how something should be.
Meine Erwartungen an den Film wurden leider nicht erfüllt.
Unfortunately, my expectations for the film were not met.

expectation
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expectation
An idea, hope, or assumption about what will happen in the future or how something should be.
Meine Erwartungen an den Film wurden leider nicht erfüllt.
Unfortunately, my expectations for the film were not met.

The noun 'die Erwartung' (expectation) is derived directly from the verb 'erwarten' (to expect). 'Erwarten' itself means 'to wait for something' and contains the word stem 'warten' (to wait). This connection helps you understand the meaning of waiting for a future event.
Wir erwarten heute Abend Gäste.
We are expecting guests this evening.
When you want to express what an expectation relates to, you use the preposition 'an' followed by the accusative. This construction is very common.
Der Trainer hat hohe Erwartungen an seine Mannschaft.
The coach has high expectations of his team.
Common verbs used with 'Erwartung' (expectation) are 'Erwartungen haben' (to have expectations), 'Erwartungen erfüllen' (to meet expectations), 'Erwartungen enttäuschen' (to disappoint expectations), or 'Erwartungen übertreffen' (to exceed expectations).
Das Konzert hat meine Erwartungen bei Weitem übertroffen.
The concert far exceeded my expectations.
To describe the state of waiting, 'Erwartung' (expectation) is often used in fixed expressions like 'in freudiger Erwartung sein' (to be in joyful expectation) or 'voller Erwartung sein' (to be full of expectation).
Die Kinder waren vor Weihnachten voller Erwartung.
The children were full of expectation before Christmas.
hope
'die Hoffnung' and 'die Erwartung' both refer to something that could happen in the future. 'Hoffnung' is positive and emotional: you wish for something good to happen. 'Erwartung' is more neutral or stronger: you expect something or think that something should be a certain way. That is why an expectation can also express pressure, while hope usually does not. The words can be confused because both have to do with the future. If it is about a positive feeling, 'Hoffnung' fits; if it is about an assumption or a demand, 'Erwartung' fits.

Die Kundin hat die klare Erwartung, dass das Gerät morgen repariert ist.
The customer has the clear expectation that the device will be repaired tomorrow.
Simon hat die Hoffnung nicht aufgegeben, dass er das Geld zurückbekommt.
Simon has not given up hope that he will get the money back.