willkommen
welcome
Expresses that a guest or person is wanted and that people are happy about their arrival.
Fühl dich wie zu Hause, du bist hier immer willkommen.
Make yourself at home; you are always welcome here.

welcome
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welcome
Expresses that a guest or person is wanted and that people are happy about their arrival.
Fühl dich wie zu Hause, du bist hier immer willkommen.
Make yourself at home; you are always welcome here.

The word 'willkommen' (welcome) is derived from 'Wille' (will) and 'kommen' (to come). So it literally describes someone whose coming corresponds to one's own will and is therefore desired.
Jeder Gast, der in guter Absicht kommt, ist uns willkommen.
Every guest who comes with good intentions is welcome to us.
As a standalone greeting, 'Willkommen' (welcome) is capitalized. When it is used as an adjective with the verb 'sein' (to be), it is written in lowercase.
Willkommen in unserem Team!
Welcome to our team!
As a greeting, 'Willkommen' (welcome) often stands at the beginning of a sentence, followed by the preposition 'in' or 'zu' with the dative to name the place or occasion.
Willkommen in Berlin!
Welcome to Berlin!
The expression 'jemanden willkommen heißen' (to welcome someone) is a fixed structure. The person being greeted is always in the accusative.
Der Rektor hieß die neuen Studierenden herzlich willkommen.
The rector warmly welcomed the new students.
When something is 'willkommen' (welcome), the word often appears before nouns like 'Abwechslung' (change), 'Gelegenheit' (opportunity), 'Pause' (break), or 'Überraschung' (surprise).
Nach der langen Arbeitswoche war das freie Wochenende eine willkommene Pause.
After the long workweek, the free weekend was a welcome break.
to receive
'willkommen' and 'empfangen' can both have to do with the arrival of guests. 'willkommen' describes that a person is wanted and that people are happy to see them. For example, you say 'Du bist willkommen' (you are welcome) or 'Herzlich willkommen' (a warm welcome). 'empfangen' is a verb and describes the action: someone greets guests or visitors, often somewhat formally. Learners may confuse the words because both occur in greeting situations. A practical tip: 'willkommen' says how the person is viewed; 'empfangen' says what someone does when the person arrives.

Bei uns bist du jederzeit willkommen.
You are welcome at our place anytime.
Die Direktorin empfängt die Gäste am Eingang der Schule.
The principal receives the guests at the school entrance.