Professor doesn't reply email even after I talked to him?
Wait. As Buffy said, a day is virtually no time at all. The professor may be trying to give others a chance to respond, or may just be busy with other things. While your zeal is admirable, overdoing it will raise red flags. If he invited applications on Monday, I would wait at least until Friday before following up. Depending on the local culture, dropping by his office in person on Friday (or the following week) may be a good idea; otherwise, I would (again on/after Friday) just send a brief e-mail saying that you are still interested and that you hope to discuss the position with him soon.