OpenGL first person jumping code
After your comment, the only change i could say is to change

private void jump(){ // called every frame
    if(jumping){
        if(y &gt;= -jumpHeight){
            y -= jumpSpeed;
        }else{
            jumping = false;
            falling = true;
        }
    }

    if(falling){


to

private void jump(){ // called every frame
    if(jumping){
        if(y &gt;= -jumpHeight){
            y -= jumpSpeed;
        }else{
            jumping = false;
            falling = true;
        }
    }

    else if(falling){


To avoid to check falling too if it's jumping. But its a macro optimization (useless too maybe in this case.)
But really, this code is perfect how it is. So go ahead!

Just got this idea in my mind: you could define a "PlayerStatus" enum with: Falling, Jumping but it will affect the logic of your game, change it only if you think you will need more status and maintain two boolean variables (or more if you add more conditions) will be hard. If you need only one turned on and others off.. it's a great way to do it:

enum PlayerStatus
{
    FALLING,
    JUMPING
}


and use the enum to change the status..

PlayerStatus status;
status = PlayerStatus.FALLING;