The subject of this Psalm is waiting for God. It is not wait and see, but expect. It is putting one's trust in God, and to do so in the strongest terms. The psalm is written in the first person singular, which means that it is a Personal Psalm. That is why it is one of the favorite psalms of many believers of all times. Psalm 62:1-2 are practically repeated in 62:5~6.
This is a Psalm of the strongest faith, in which the experience of hostility (62:3-4) and the contemplation of life (62:9~10) only provide the background against which a serene confidence in God displays itself. Its tone is not inconsistent with the character of David, who " encouraged himself in the LORD his God" (1Samuel 30:6).
The question "how long" (v. 3) is not the sigh of someone burdened by enmity. It is the expression of one who is in silence for God. From God's presence David asks the assailants how long they think they can go on doing it. It is not a fearful, but an almost challenging question: "How long do you think you can continue?" What is described in these two verses (62:3-4) of the devisers of evil, the Lord Jesus experienced in the fullest way. He is the "man" (v. 3) Whom they assailed constantly. We should not be surprised if the world also hates us (1John3:13). The world hated the Lord Jesus (John 7:7) and therefore will also hate us (John 17:14). The believing remnant in the future will also experience this from the unbelieving Jews and the demonic Islamic invaders.
Expectation implies dependence based on the understanding that we can do nothing without Him. It also implies trust in faith that God's time is the best time and therefore we wait for Him and expect it from Him. It is trusting in Him that He will certainly come and in the right time, way and place. Through this, perseverance also gets a perfect work in us (James 1:4).