I've heard of this method of eating--which we all normally do anyway, since some days we're just hungrier and more active than other days, so the logic in doing it is totally there--but I've never heard of it being like alternating between maintenance-calorie days and super-low-calorie days.
What I've seen at Sparkpeople is people who alternate between higher-calorie days, maintenance-calorie days, and lower-calorie days, so something like Monday=2000, Tuesday=1000, Wednesday=1500, etc., so that overall, it adds up to no more than 3500 calories less weekly for 1 pound of weight loss from calorie restriction alone. Eating only 500 a day is detrimental and will definitely leave you starving by the end of the day, making you very vulnerable to giving up and just binge-eating.
That said, I would say drink more water (we often confuse hunger with thirst), ask yourself if you're definitely hungry (are you so hungry that you'd eat a plain cucumber if that was all that was available, or do you really just have a craving for a fatty/sugary food?), and carry small snacks with you like an orange/banana/apple, a mozzarella stick, or a small handful of almonds or other nuts in a small ziploc bag.