
sehnsüchtig
longing
Filled with a strong desire or longing for someone or something.
Sie wartete sehnsüchtig auf einen Brief von ihm.
She waited longingly for a letter from him.
longing
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longing
Filled with a strong desire or longing for someone or something.
Sie wartete sehnsüchtig auf einen Brief von ihm.
She waited longingly for a letter from him.
The word is derived from 'die Sehnsucht' (longing). This noun is itself an intense combination of '(sich) sehnen' (to long for) and 'die Sucht' (addiction). So it describes an almost addictive desire.
Mit sehnsüchtigem Blick schaute er dem abfahrenden Zug hinterher.
With a longing look, he watched the departing train.
'Sehnsüchtig' (longing/longingly) can stand before a noun as an adjective or describe an action as an adverb. As an adverb, it often modifies verbs of waiting, looking, or thinking.
Er schrieb ihr einen sehnsüchtigen Brief.
He wrote her a longing letter.
'Sehnsüchtig' (longing/longingly) is very often combined with verbs of waiting or expecting. A typical collocation is 'sehnsüchtig auf etwas warten' (to wait longingly for something).
Die Kinder warten sehnsüchtig auf den Weihnachtsmann.
The children are waiting longingly for Santa Claus.
nostalgic
Sehnsüchtig describes a strong longing for a person or thing and can also refer to something in the present or future. Nostalgisch specifically describes an often idealized and sentimental longing for the past. Nostalgisch is therefore more precise when talking about memories.

Sie blickt sehnsüchtig auf das Foto ihres Partners, der morgen zurückkommt.
She gazes longingly at a photo of her partner, who is coming back tomorrow.
Sie blickt nostalgisch auf die Fotos ihrer längst vergangenen Schulzeit.
She gazes nostalgically at photos from her school days long ago.